Sounds like the leaks you found are fuel. Check the plug in the rear injector, they commonly start leaking.
If you don't find any oil leaks after you've repaired the fuel leaks, you may need to put valve stem seals in it. If the engine starts easy and runs good, and it is indeed using lots of oil, it is probably coming past the valves. If the rings get bad enough to pump oil, the engine usually will get very difficult to start as well.
'84 Euro 240D, 523K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in