If it were me, before you do anything else, I would check that the inner axle bolts aren't loose or missing.
Seen in this image on the left. They attach the axle to the transmission.
If they are present and tight, then I don't know.
Maybe the outer CV joint? I don't know what those would cost new, but if it turns out to be that I bet you could get a good used one from Woody (ItsNotaNova) at a decent price.
Might try jacking up the rear wheels, and with the front wheels chocked, put it into gear and see if it will make the noise with the wheels spinning but not under load. Whatever you do don't get under the car!