Most places will just suck out whatever oil they can through the fill hole as well, especially for the front. Just get a heavy duty hand pump for the auto parts store, they are usually with the gear oil.
For the rear you can pull the diff cover. Remove all of the bolts and gently pry the cover off without scratching the axle mating surface. Pull it off and let it drain. Get a spray can of silicone gasket remover, spray it on the mating surfaces and scrape it off with a plastic scraper tool. Wipe everything dry. Apply new RTV gasket around the mating surface (not too heavy) and follow the instructions. Probably set it on there and loosely install the bolts, let it setup for an hour or more. Then torque the bolts down, and refill from the front until it flows out.
You should also make sure you can remove the fill plug on the front of the diff BEFORE pulling the cover.
2006 F150 FX4 Super Crew - Bilstien 5100s leveled 2", 35" KM2s, 4.56 gears, Detroit locker, Eaton E-Locker, Traction Bars, AEM intake, Xcal 2
2010 VW Golf TDI 6MT