How powerful must a gravitational wave be, to be audible to a human? Sufficiently powerful gravitational waves can excite an eardrum and be heard. How powerful would the waves have to be for a human to actually hear them, and what would be the side-effects of that intensity of gravitational radiation?
 A: No, not really. There are a number of factors for why you can't:

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*As duly pointed in the comments, you 'hear' something when the eardrum moves with respect to i.e. differently from your body. If you are in the middle of a wave, then you body is deformed in the same way as your eardrum. Also, there is the fact that the disturbance caused by the waves themselves are in the order of magnitudes of the size of an atomic nucleus. There is no way our eardrums can detected that (more on that in point 2). So, you can't hear the wave itself.

*Gravitational waves tend to have very low frequencies (corresponds to long wavelengths). According to an answer here, the maximum frequency of a gravity wave is proportional to $\sqrt{G\rho}$, where $\rho$ is the density of whatever object released the waves. Waves which have longer wavelengths just pass through an object smaller than it's wavelength (Though it has been pointed out in the comments below, that we can hear sounds of wavelength $17$m). Keeping in mind the usual wavelengths of gravity waves, (and the size of the ears), to hear a gravity wave would require a ridiculously large amount of energy. The disturbance caused by any regular gravity waves is in the order of magnitudes of an atomic nucleus. Our eardrums are not built to be that sharp. So, if the gravity wave has to 'disturb' our eardrum, it needs humungous amounts of energy.  And that energy has to be produced by something having $\rho$ more than anything we have ever detected or hypothesised. (And such an event of high energy, may as well destroy Earth itself; not by gravity waves, but by other forms of radiation or free energy)

*The most important point: gravity waves don't work that way. The eardrum vibrates when any sound wave applies pressure on it. Gravity waves are not like conventional waves: they don't apply a pressure on anything. In fact, they just stretch and compress space itself, and that does not inflict any pressure on an object. If your ear is anywhere near a gravity wave, the eardrum would be squished and squashed, which is not the equivalent of a vibration caused by a sound wave. If you want to know more about how the gravity wave stretches and compresses space, take a look at my answer here: How can we imagine gravitational waves?
So, that is why you could not 'hear' gravitational waves.
