Over-arousal in certain brain areas is linked with anxiety disorders, sleep problems, nightmares, hyper-vigilance, impulsive behaviour, anger/aggression, agitated depression, chronic nerve pain and spasticity. Under-arousal in certain brain areas leads to some types of depression, attention deficit, chronic pain and insomnia. A combination of under-arousal and over-arousal is seen in cases of anxiety, depression and ADHD. more...
So, in summary, binaural beats certainly do not work the way the sellers claim, but there's no reason to think they're any less effective than any other music track you might listen to that effects you in a way you like. If they make you sleepy (like they all do for me), use them to go to sleep. If they relax you or get you amped, use them for that. But don't expect them to be any more effective than regular music. If someone you know claims that they are, put them to the test, and bust the myth.
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Isochronic tones work by influencing your brainwave activity and they can’t directly affect the body. That said, the brain does control the body, so sensations and feelings can sometimes be felt in the body after stimulating your brainwave activity. Some people who are new listeners of this type of audio can sometimes feel tingling sensations in their body. Not everyone feels this and these sensations usually stop once you get more used to using the audios. Isochronic tones are considered as a safe technology. However, sometimes they can leave you feeling temporarily fatigued, especially if you listen to them for an extended period (hours) when you first start using them. If you felt fatigued, I would recommend using them for a much shorter period while you are getting used to them and ensure you are well-hydrated.
I wouldn’t personally recommend listening to delta wave frequencies for depression, so I’m not sure who advised you to do that? People with depression usually have a higher ratio of theta and delta wave activity, so I would normally recommend listening to high alpha wave and low beta wave frequencies, to help balance things. I have some 10Hz alpha tracks for serotonin release, which you can try for free on my YouTube channel here: https://www.youtube.com/watch?v=3NSUcuzpRcY&list=PLveg0IEcZWN6T86nhmSrdwG2kMQtcLRou. I also recommend you give these SMR (low beta wave) tracks a try: https://www.youtube.com/watch?v=HGTvBbrEwZQ&list=PLveg0IEcZWN7yaMaKr8F-eWHALk2_zGqY. I hope that helps.
They came to the table with the idea that the entrainment track would “cause” them to be in meditation, which it doesn’t. Or they thought that having the specific brainwaves the entrainment program promotes would “cause” them to be in meditation. It doesn’t. If you really understand the principles above, you’ll understand why. If you don’t grasp why yet, read these principles again and consider what they really mean. The answer is there.

With regard to listening without headphones specifically, you might find it irritating if you are someone who suffers from motion sickness, depending on how the track is created. If you were listening to binaural beats, they really need headphones to work properly. If you are in a room and closer to one speaker you may not even hear binaural beats properly, and if sitting off centre in the room generally, that may have unsettled you if you have motion sickness as the tones try to form a beat in your head. If it was just a standard isochronic tones theta track that shouldn’t be irritating if you have motion sickness.

Controversies concerning the brain, mind, and consciousness have existed since the early Greek philosophers argued about the nature of the mind-body relationship, and none of these disputes has been resolved. Modern neurologists have located the mind in the brain and have said that consciousness is the result of electrochemical neurological activity. There are, however, growing observations to the contrary. There is no neuro-physiological research which conclusively shows that the higher levels of mind (intuition, insight, creativity, imagination, understanding, thought, reasoning, intent, decision, knowing, will, spirit, or soul) are located in brain tissue (Hunt, 1995). A resolution to the controversies surrounding the higher mind and consciousness and the mind-body problem in general may need to involve an epistemological shift to include extra-rational ways of knowing (de Quincey, 1994) and cannot be comprehended by neuro-chemical brain studies alone. We are in the midst of a revolution focusing on the study of consciousness (Owens, 1995). Penfield, an eminent contemporary neurophysiologist, found that the human mind continued to work in spite of the brain's reduced activity under anesthesia. Brain waves were nearly absent while the mind was just as active as in the waking state. The only difference was in the content of the conscious experience. Following Penfield's work, other researchers have reported awareness in comatose patients (Hunt, 1995) and there is a growing body of evidence which suggests that reduced cortical arousal while maintaining conscious awareness is possible (Fischer, 1971;West 1980; Delmonte, 1984; Goleman 1988; Jevning, Wallace, & Beidenbach, 1992; Wallace, 1986; Mavromatis, 1991). These states are variously referred to as meditative, trance, altered, hypnogogic, hypnotic, and twilight-learning states (Budzynski, 1986). Broadly defined, the various forms of altered states rest on the maintenance of conscious awareness in a physiologically reduced state of arousal marked by parasympathetic dominance (Mavromatis, 1991). Recent physiological studies of highly hypnotizable subjects and adept meditators indicate that maintaining awareness with reduced cortical arousal is indeed possible in selected individuals as a natural ability or as an acquired skill (Sabourin, Cutcomb, Crawford, & Pribram, 1993). More and more scientists are expressing doubts about the neurologists' brain-mind model because it fails to answer so many questions about our ordinary experiences, as well as evading our mystical and spiritual ones. The scientific evidence supporting the phenomenon of remote viewing alone is sufficient to show that mind-consciousness is not a local phenomenon (McMoneagle, 1993).  
Binaural beats are acoustically generated frequencies that match the frequency bands of brain waves and are therefore considered a means to inducing neurophysiological relaxation. There is, however, large dispute on the scientific quality and validity of extant research on binaural beats. Thus, the effect of a binaural 10Hz (Alpha) stimulation on subjective and physiological parameters... [Show full abstract]
Gaia Meditation Delta programs are specifically designed to: improve sleep and healing process. Effects happen at a very deep subconscious level, ideal for powerful reprogramming. If you’re in lack of sleep because you’re a busy business man or because you have insomnia etc., a few hours of our Delta waves programs will trick your brain into thinking it had all the restorative sleep it needs.

Another common misconception is that entrainment is going to force your brain into doing something beyond its native capabilities, or at least beyond what it is accustomed to doing. This mistaken belief is often the root that leads to comments like, “When I meditate with LifeFlow my face gets flushed (or my hair vibrates or I develop x-ray vision, or any of the other things we come across). If I meditate without LifeFlow the face flushing doesn’t happen. LifeFlow must be causing it.”
♥ I've suffered from patches of insomnia throughout my life, extending from a few days to dragging on for several weeks, and no amount of the usual proper "bedtime ritual" normally recommended, calms me, as my brain is overactive. Layering combos of the Binaural/Bilateral sounds right before sleep effectively resets me, allowing me to sleep like a normal human. I can't express enough gratitude!
Slightly higher-frequency entrainment can lead to hyper suggestive states of consciousness. Still higher-frequency EEG states are associated with alert and focused mental activity needed for the optimal performance of many tasks. Perceived reality changes depending on the state of consciousness of the perceiver (Tart, 1975). Some states of consciousness provide limited views of reality, while others provide an expanded awareness of reality. For the most part, states of consciousness change in response to the ever-changing internal environment and surrounding stimulation. For example, states of consciousness are subject to influences like drugs and circadian and ultradian rhythms (Rossi, 1986; Shannahoff-Khalsa, 1991; Webb & Dube, 1981). Specific states of consciousness can also be learned as adaptive behaviors to demanding circumstances (Green and Green, 1986).  
Gaia Meditation Gamma programs are specifically designed to: stimulate cognitive functions, help for higher learning and greater focus, improve IQ, expand consciousness and inspiration. The Dalai Lama meditates 4 hours every morning, which must stimulate his Gamma activity in a tremendous way. However, even if you have never practiced meditation, our Gamma waves programs will take you easily and rapidly to the Gamma brain state.
A study by Tina Huang, PhD, and Christine Charyton, published in the September 2008 issue of the journal, Alternative Therapies examined the results of twenty previous studies measuring the effectiveness of brainwave entrainment for improvements in cognitive dysfunction and deficits, stress reduction, pain management, migraine and headache control, pre-menstrual syndrome, and behavioral difficulties, and all showed significant improvement in symptoms using entrainment techniques.
Infra-Low brainwaves (also known as Slow Cortical Potentials), are thought to be the basic cortical rythms that underlie our higher brain functions. Very little is known about infra-low brainwaves. Their slow nature make them difficult to detect and accurately measure, so few studies have been done. They appear to take a major role in brain timing and network function. 
This research investigates the brainwave entrainment process and aims to demonstrate the usefulness of such an approach within the framework of cognitive performance improvements. In the introductory part the theories regarding the neurophysiological structure and the psychological processing of the cognitive system are discussed, for each of their components that are considered to be relevant for this research. The hypothesis states that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition. The research variables are the cognitive performance (the dependent variable) and the brainwave entrainment (the independent variable). The brainwave entrainment program consists in the synchronized application of Alpha binaural beats and stroboscopic light, at a 10.2 Hz frequency, in a 30 minutes long session. The difference was made by the stroop effect based exercise that was used as a frame. There were 60 participants, divided into two independent samples. The two independent samples t test for the means differences was used in the statistical analysis. The obtained results by evaluations and by statistics confirmed this research's hypothesis, stating that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition.
... The goal of the study was to observe the effect of exposure to BB on working memory capacity. As suggested by many studies, BBs corresponding to alpha brain waves can positively influence cognitive processing, namely attention, auditory sequential memory, working memory, working memory storage, and reasoning ability (Carter & Russell, 1993;Cruceanu & Rotarescu, 2013;Foster, 1990;Kennerly, 1994;McMurray, 2006). The results show that a BB of the frequency of 9.55 Hz – which is a representation of the alpha frequency range of the brain activity – had a temporary positive effect on working memory capacity in our sample of healthy, adult university students. ...
The studies included in the recent reviews of Tai Chi and yoga indicate that sessions between 60 and 90 minutes performed 2 to 3 days per week were effective in reducing stress and improving feelings of well-being (7,14,17). A study conducted in a worksite environment showed that 15 minutes of chair-based yoga postures was effective in reducing acute stress when assessed by self-report and with physiological measures (e.g., respiration rate and heart rate variability parameters). This finding indicates that shorter duration sessions can be effective in reducing acute stress with this type of exercise (15).

You are already far beyond the need for using an entrainment product as a meditation aid. Those who sincerely believe this to be the case would not have come searching for a meditation site such as Project Meditation to help them learn and practice meditation and brainwave entrainment. They would probably not even bother with using an entrainment aid; hence this entire discussion would be irrelevant to them. The fact that you are here, reading this, seeking to benefit from incorporating meditation and brainwave entrainment to aid in your existing meditation practice suggests you are not one of these folks whose development is so advanced that entrainment is of no use to you.

With brain wave entrainment technology, changing brain wave states is an instantaneous and effortless process. The 'periodic stimulus' can be sound, vibrations and/or light. We have found that we get the best results with blinking lights which are experienced through closed eyelids. This is only problematic for people with existing diagnosis of photo-induced epilepsy, as blinking lights can induce a seizure in them. The programs are enhanced with Deepak Chopra doing the narration along with holographic sound effects and original music composed and performed by Rudy Tanzi.
Brainwave entrainment is a colloquialism for such 'neural entrainment', which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of an external stimuli, such as a sustained acoustic frequency perceived as pitch, a regularly repeating pattern of intermittent sounds, perceived as rhythm, or of a regularly rhythmically intermittent flashing light.