Take the gears out, and get as much oil out as I can by wiping with paper towel. flip the diff case upside down on a paper towel and let it sit for a while.
The I use /nitro clean on the gears and outdrives. After two "rounds" of spraying, I blow them off with some compressed air. Look good as new!
Then I blow out the diff case with the compressed air as well. Leaves a very thing layer of oil in the case, but I highly doubt it makes a difference. I don't like using any chemicals to the clean the case out because I don't want it to mix at all with the diff oil if any is left behind. It's hard to get all of the oil out even after spraying anyways because of all of the nooks and crannies in there.