Start cheaply: drain the old oil out. No need to remove the cover, just pull the bottom (6 o'clock) bolt out - that serves as a drain. Clean off around the fill plug and remove it as well.
Refill with fresh gear lube (GL5 in 90 weight; 80W in cold zones) AND add the limited slip oil additive. Most parts stores carry it; comes in about a 4 oz tube. You'll need close to a quart and a half of gear oil for the diff, but add the LSD additive before you top off the diff.
Back when my '92 245 was new to me, I changed all the fluids without knowing I had a No-Spin diff. The axle started banging on tight turns (like a corkscrew ramp in a parking garage) - scary sounding! Eventually I found the tag on the diff telling me what I had. So then I did my research and put in Mobil 1 gear lube, supposedly fine for limited slip axles, no additives needed... WRONG! Once I changed to regular gear lube and the additive, all was well.
You might be having other problems, but your symptoms sound exactly the same as what I experienced.
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