I'm assuming there is a hole in the trans case if there is oil all over under the car. Have you visually confirmed this to make sure it's not simply a leaking seal or a leak between the case halves?
If it has put a hole in the case you're going to need a new case, not to mention there is probably metals chips all over inside the trans that could cause a lot of other damage later. At the very least the trans will have to come out, be disassembled and cleaned.
FWIW here is the VFAQ for center diff replacement.