Would you hear a gravitational wave, if its amplitude and frequency were suitable?
The frequency of the recent experiment was in the audible range. The amplitude was off by unspeakable orders of magnitude. But yes, you would hear it (even in vacuum, if you were to survive).
Yes, the GW are transverse (quadrupolar). But they do move things (they cause change in distances, that's actually how they detected them: the length of the 4km tube at LIGO changed; earlier experiments actually planned to detect the "sound" of a vibrating metal cylinder, but they weren't sensitive enough). An eardrum and the bones around them are a complex instrument and whatever direction the strain is applied, it would surely induce a vibrational motion that would produce vibration of the eardrum, even if not in the way you imagine (compare to sound, where there is direct pressure to the eardrum -- GW are more profound and make the eardrum itself directly deform and vibrate). If you were close enough to a cataclismic cosmic event, you would hear it across the emptiness of the space. Both directly (as induced vibrations in our bones), and through creaking of the structures around us.
It's interesting to note that generally the same instrument that was used more than a century ago to prove that velocity of the "aether" is impossible to detect (disproving the notion of an elastic medium permeating the universe) was now used to prove acceleration of the "aether" (so to speak) can and was measured.
Lets look at the problem on a quantum mechanical level. Sound is generated by vibrating atoms in a solid transferring their energy to the air, and the energy moves in sound waves and reaches our ears or instruments. This happens with the exchange of electromagnetic interactions, at a complex level, but still photons and scatterings are involved.
A gravitational wave is composed of gravitons, but the coupling constant is very very much smaller than the electromagnetic one. There is no transfer of energy to the lattices of the solid that could change the pressure and generate sound waves. It passes as is, without losing energy, through our eardrums too because of the extremely weak coupling with matter.
From wikipedia:
The effects of a passing gravitational wave can be visualized by imagining a perfectly flat region of spacetime with a group of motionless test particles lying in a plane (e.g., the surface of a computer screen). As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles (i.e. following the observer's line of vision into the screen), the particles will follow the distortion in spacetime, oscillating in a "cruciform" manner, as shown in the animations. The area enclosed by the test particles does not change and there is no motion along the direction of propagation.
https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:GravitationalWave_PlusPolarization.gif