First off, I'm not sure there's anything wrong with your rear derailer save adjusting the limit screws. Your derailer hanger (thelittle part of the frame that attaches to the derailer), might be bent and need to be straightened. Without looking at the bike, I can't really tell what's wrong.

I'd suggest taking the bike to a shop and getting it tuned up. You'll want to make sure the spoke tention is high enough-- you can destroy the wheels by riding on loose spokes. You might need a new chain and freewheel. The bearings in the hubs, bottom bracket or headset may be dry or loose. It's going to cost over $150 for a good rebuild+parts. Let the pros help you get your bike on the road.