I can say with a HIGH DEGREE OF CONFIDENCE, that it'* engine oil WICKING up the BOLT THREADS of the LIM.
1) Go to your local auto parts store and purchase a tube of PERMATEX 2B. It is a very dark brown thick cream.
2) Remove the LIM bolts one at a time (so as to not upset the torque across the LIM) and wipe the threads clean with a towel. Afterwards, you can wire brush the threads with a wire brush.
3) Apply a generous amount of 2B to the threads of each LIM bolt (just the ones that are leaking oil) and wipe off the excess with your finger.
4) Install the freshly coated LIM bolt into the threaded hole and tighten. I use a 10mm swivel socket with a long 1/4 drive extension with a 1/4 drive ratchet, but you can use a torque wrench if you want to. (132 inch pounds) or as tight as you can get it with a 1/4 drive ratchet.
5) You can clean up the oil residue down in the LIM valley with some gauze on the end of a pair of hemostats. You can substitute the hemostats with a long pair of needle nose pliers if need be.
Why does this happen? Because the 3800'* have an awsome oil pump with outstanding oil pressure.
Author'* Note: Permatex 2B is God'* gift to mechanics.
Make sure it says 2B.... not 1A like this photo.