"I tried removing the differential fill plug to see how much oil is in the diff. but the hex socket on the plug is misshapen and I can't get a grip with a 14mm Allen head socket."

Yeah,that's gonna be a Bugger!
'Some have used a "Come Along" attached to the Jack to move the Wrench
(AND the Plug)

If (As I understand your description) the internal Hex of the Plug is Messed Up
...See if Sears or one of the "Tool Trucks" have the equivalent of an "Easy Out"
for the internal hex.
I am NOT going to suggest you drain the Diff and braise the 14 mm Allen into
the Messed up hex.(Too much chance of Involuntary Combustible "Incident".)
Although,(God Forbid) you may come to removing the Diff and taking it to
a Machine Shop so They can!

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'84 300SD sold
124.128