According to a 1948 paper by Bekesy [0], a human ear can detect sounds through several mechanisms. In a gravitational wave, since the whole head would vibrate, sound would reach the ear by bone conduction through the skull. Fortunately, this also happens to be the most sensitive mechanism. The smallest vibration amplitude detectable by bone conduction is about 4 x 10^-9 cm at around 3 kHz. If a typical skull is about 17.5 cm from front to back, that gives a minimum detectable wave amplitude h (the fractional expansion and contraction of spacetime) of about 2 x 10^-10.
The frequency of the gravitational waves produced in a collision between a neutron star and a small black hole turns out to be pretty close to an optimal match for the human ear. To estimate the amplitude, the first black hole collision detected at LIGO produced a strain of about 10^-21 at a distance of 410 Mpc. (The events in the article were smaller, but within the same order of magnitude.) Thus, since the amplitude scales as 1/r, the gravitational waves from the collision in the article would have been theoretically audible at a distance of about 400 AU or 40 billion miles.
Alas, attempting to test this calculation experimentally would incur certain practical difficulties. Notably, you would be vaporized by gamma radiation from the collision several seconds before the gravitational waves became audible.