Looks like the axle stub shaft seal is toast. I would guess its a standard seal, so you can get the dimensions from the seal itself, and order a replacement. Don't let the oil run low.
I am not familiar with the assembly of the MB/oberaigner front diff. Its possible that the axle stub shaft is held in with a spring clip. So it can be removed with a slide hammer. If so you can replace the seal with the diff installed.
You can check the parts catalogs (subscription required unfortunately). Last I checked, they didn't break down the trans. A dealer may be able to help, may be worth a call. There are a few users here with STAR laptop units which contain the EPC data, one may post up offering to help.
Boot,
That does not look like gear oil to me. Give it a wash to find the leak. Could be the turbo. There is no listing of parts for the diff, I have rebuilt a couple, the seals were standard bearing shop no delays.
Eric.
Boot
The reason I asked is that if the diff had water in it then that would explain the oil exit when hot, if the vent was open then the oil should have exit the vent. Eric.