That's a aftermarket "muffler" ....but I don't really see any oil on pipe joints, the wet look may just be condensation, have you ran it a while before this pic was taken?
Check oil / coolant level & start it up, use the cruise switch and bump rpm up to 11/1300 for 30/45 min.
Note any smoking from exhaust and blow by at crankcase vent hose, it'll be a 3/4" or so hose that runs down right beside oil filter, may have to get under coach to see it.
1999 American Eagle
ASE med/heavy certified technician
ASE advanced diesel certified