I've seen that just a few times in my day. Simple enough ...
Put the bike on a stand and check for bearing wear. If the bearings are that far out of spec, you should notice more than just a "wobble". Using the clock as a guide, grab the wheel at 9 & 3, and check for play, and again at 12 and 6, watching to make sure the swing arm isn't moving (which would indicate suspension wear). If everything seems "tight" there, the next step is to give the wheel a spin and watch for rim warp. Having a buddy hold the bike still on the stand is always a good thing. Sit behind the bike, and give the wheel a good spin and watch for the "wobble". Chances are, either the rim has taken a serious bend, or someone played around with tightening the spokes and took it badly out of "true".
I had a riding buddy that went through this, and he ended up having to buy another wheel. With the age of your bike, you should be able to find one at a reasonable price.
Best of luck!