I worked this out once!
Gravitational waves obey the inverse-square law much like most radiation does (and subject to some constraints about weird spatial geometry, but most of their propagation is going on in open flat-ish space, so we can ignore that).
GW150914, the first gravitational wave observed, had an amplitude of about 4 times 10^-22 [1], i.e., differences changed by a factor of about that. Typical sound displaces the eardrum by on the order of half a micron or so [2], with the threshold of hearing at about 100 nm. The inner ear's shape is curved, but linear length is on the order of 10 mm [3] (it curves around so the total length is longer, but the gravitational wave would be transverse along its length).
A 100 nm displacement on a 10 mm length is a relative change of (100 x 10^-9) / (10 x 10^-3) = 10^-7, that is, 4 times 10^-17 times larger than the gravitational wave detected. That gravitational wave was emitted at a distance of about 410 Mpc [1], and so we can solve:
(d / 410 Mpc)^2 = 4 x 10^-17
d^2 = 4 x 10^-17 * (410 Mpc)^2
d = 2 parsec.
Granted, this is at the limit of hearing for a very brief sound (the sound was only in the human audible range for about a tenth of a second). You'd need to be perhaps 10 times closer - about 20,000 AU - for it to be a loud sound under these assumptions.
Of course you wouldn't be around to hear it for very long because you're 20,000 AU from one of the most energetic events in the cosmos, but hey, you'd hear a brief "click". Totally worth being vaporized.
[1] https://en.wikipedia.org/wiki/First_observation_of_gravitati...
[2] https://biology.stackexchange.com/questions/79963/how-far-do...
[3] https://www.verywellhealth.com/inner-ear-anatomy-5094399