I have a Dana 44 which has a metal/magnetic drain plug that collects all of the metal debris and requires a 3/8" drive extension to loosen. So, when the oil has finished draining, I retighten the remaining cover bolts by hand and loosen the drain plug. Then I remove the bolts and differential cover.

The gears and inside of the differential can be cleaned a spray can of brake parts cleaner or carb cleaner. While that continues to drain I try to clean up the drain plug, cover and cover bolts with more parts cleaner and a wire brush.