Looks to be a gasket failure to me as well.
Its not that difficult to fix.first the parts:
Parts from dealer:
diff housing gasket(thin paper)
diff drain and fill gaskets(2)
(1) tube FIPG PN:08826-00090,orange sealant(could use "right suff"as well).do not use rtv
If you want to do axle seals,now is the time to do them:
axle seals (2)
Parts from auto store:
4 quarts gear oil.
generic vacuum plug/cap assortment
roll of blue towls
2 cans brake cleaner
highly reccomend some nitrile gloves
ok,have parts..lets begin:
loosen rear lugs,jack rear,secure w/stands,put in neutral.
drain gear oil.
Take a scribe or tuchup paint,tire marker,ect.paint/scratch a line at diff flange and drive shaft(to keep it in phase)
Remove driveshaft from diff flange,slide driveshaft out of trans.(4 bolts and nuts at flange)
Remove e-brake cables(clips) from both side backing plate.
Remove 4 nuts that attach brake backing plate from axle housing,both sides.
Unscrew brake lines from wheel cylinders (must use 10mm LINE WRENCH)....Brake fluid now will leak from line,have some vacuum line caps on hand to put over brake line,so you don't run out of brake fluid.
Remove axle assemblies(will just slide out from axle tube)..carefull not to rest axle on seals if reusing them.
Remove all but 2 nuts(leave loose) that attach the diff to the axle assembly....GENTLY tap side of diff(3rd member) with soft face hammer,might have to use a pry bar(go easy) to get it to seperate from axle assembly.
Diff. is now resting on axle housing studs,remove the two remaining nuts(should be finger tight).
Remove diff. from axle assembly.
Remove old paper gasket(get every piece) from diff and/or axle assembly.
clean up sealing surface,diff side and axle side.
clean up diff,axle assembly w/ brake clean.
Put a LIGHT coating of FIPG(orange) or "right stuff" on both sides of paper gasket.
Place paper gasket on axle housing studs.
Now is a good time to tackle axle seals,once diff is in.
Now its assembly time.......Installation is reverse of disassembly.
Do not over torque diff nuts..(my rule of thumb)equivilant to 1/4 ratchet,tight as you can do with one hand.
If a stud comes out of axle assembly when you are taking it apart,when you put it back use a little bit of sealant on threads.
Make sure you get drive shaft bolts tight,touch of blue thread lock is good insurance,same with the 4 axle flange nuts.
Don't rest axle shafts on seal when you are assembling(carefull not to nick them as well)
Don't forget to put gear oil back in.
Don't froget to put in PARK before you lower it off the stands.
Don't forget to bleed the brakes and check the brake fluid level,before the test drive.
Its going to be a messy job,need to have a couple of catch buckets on hand...And you will thank me for the nitril gloves