Diff throwing oil

Looks to be pinion seal gone - mark alignment of prop shaft to pinion flange, undo the four bolts and drop prop shaft, mark alignment of a. pinion nut b. pinion flange and c. pinion, undo pinion nut carefully counting number of revolutuions, put container under the pinion flange to catch the diff oil, remove drive flange, remove pinion seal, fit new pinion seal, refit drive flange carefully aligning marks made prior to removal on b. pinion flange and c. pinion, refit pinion nut taking care to wind on same number of revolutions and correctly align to the marks you made before removal on a. pinion nut b. pinion flange and c. pinion, refit four prop shaft bolts taking care to align marks on prop shaft and pinion flange prior to removal, refill diff fluid (I have been using LSX90 on open diff centres for 20 odd years with no issues).
 
While ideally you would remove the diff centre and reset pinion preload on the bench as long as you are careful in relainging the marks in the above process you should not have any issues. 
 
I have on rare occasions had oil leaking around the pinion nut; easly spotted by any oil dropping out when you split the prop shaft from the pinion flange. In these cases a smear of silicone across the face of the drive flange before refitting the propshaft had fixed that issue.

The first thing to do is check fluid level in diff and top up if low. This might promote more/fresh leakage, especially if the level is very low. Degrease & clean as Gdub suggests then check for fresh leaks at either the pinion seal, leaking past the pinion nut and the mounting flange after a decent drive. 
rgds,
SFE