I would start by popping off a rear wheel and looking at the condition of the:
brakes - even a half warn brake shoe can sound bad, or be off kilter, or wear unevenly. Does it pull to either side?
bearings - Luckily they are just regular old school bearings back there, pull the drum, pack the bearing (or replace it) but pack it good.
u-joint - I thought I didn't have any u-joint problems, but was having a "clunk" when taking off or stopping. When I checked my u-joint (rear) I found mangled metal, I was surprised it still worked at all, about an inch of side to side play.