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First thing to do is change out rear end lube and be sure to put two bottles of the GM posi lub in, then do figure 8s in a parking lot and see if it goes away.
Could be the Ujoints, or the posi unit. Also might be the stub axles in the posi, check to see if there is in and out movement. If there is the stub axles are worn and the rear should be rebuilt.
The first thing to check, which is the easiest and most likely is the problem, is the differential fluid. It contains special additives for the posi traction clutches built into the diff. The fluid most likely needs changing. You can buy a "rose" gun which is simply a device to suck the old fluid out thru the refill plug on the diff and add new fluid including the special additive. This should cure the problem. One way to check for this is to drive slowly in figure eights in a parking lot. If you hear the noises you referred to this is usually the problem. New fluid with the additives allow the clutches to slip during turns and as the fluid wears it finally gets to the point where the clutches will not slip anymore. Or you can go to a chevy dealer and have them change it for you. Either way it should solve your problem. Good luck with your vette!