Hm. I'd say, open the hubs and take a look at the bearings (assuming you have cup and cone bearings). Look at
http://sheldonbrown.com/cone-adjustment.html
If you see any pitting (most probably on the cones), the hubs are shot. You could try to find replacement cones (good luck with that), or replace the wheel with a new hub (how good are the rims?) or buy a new wheelset. Hubs range from 10 (dunno, 13USD) for simple front hubs and 15 for entry level rear hubs to about infinity. Rims are also in that range (<20 for a simple, box rim, ~30 for a Mavic CXP). Wheelsets (nice, entry level, robust) start in the 100 (130 USD) range. I think it is difficult to build a wheelset yourself for this price, since decent hubs + rims + spokes are not much cheaper, I like doing it, though.
Concerning the bottom bracket, look at
http://bikeride.com/check-bearing-wear/
it is a nice method. Bottom brackets start also around 10. Removing them (well, the fixed cup on the left) can be a hassle, be warned.
Also check whether the chain is gummed up, depending on how you treat your chain (lubricants etc.), gunk will collect on it. Removing it helps quite a lot (as Dave mentioned).