Scott,
If the posi still works, then all you need to do is put some fresh gear oil and friction modifier in. Buy three qts of fluid. This can be messy and stinks to high heaven but it's easy enough to do in your driveway. While your under there, check all of the seals, pinion shaft seal and axle bearing seals. If any of these are bad (leaking), it can be quite involved changing them. If nothing seems to be leaking, then you may want to remove the drive shaft and tighten the pinion nut (27mm?). Most likely it will be loose. Get a large pipe wrench to hold the pinion flange and have a buddie hold it for you. Tighten the nut (alot of force) about a 1/16 of a turn. Make sure you use loc-tite on the driveshaft bolts. That should be about it.
Keith