Looks like your run of the mill old differential to me, nothing too frightening. If there is some actual sludge in the bottom of the housing simply scrape it out and feel free to clean things with a solvent like brake cleaner if you want. Just make sure that you give it plenty of time for any solvents to evaporate before putting it back together.

Your differential lasted over 20 years with gear oil that is not as good as the stuff you can get now. Fill it it up and drive it. If you really want to do something just change it out after a hundred miles or so and you'll get out any remaingin dirt in there. It only takes a quart to fill it up and less than an hour to drain and fill it. If you are going to do that start out with plain old gear oil and then put whatever name brand or sythetic oil during the refill.