Remove and check your belly pan if you have one (most W124s do). Often when the engine leaks badly the oil just drips onto the belly pan and dries up into a film of sludge. The belly pan can be masking your oil leak. Common leak areas are the upper front engine cover, valve cover gasket, and believe it or not the oil cap seal.

Your oil loss is probably the result of both oil leaks and worn valve stem seals. Personally I would fix the leaks as doing so may reduce the oil loss to a manageable level. Replacing the valve stem seals is more work.

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08 W251 R350
97 W210 E320
91 W124 300E
86 W126 560SEL
85 W126 380SE Silver
85 W126 380SE Cranberry
79 W123 250
78 W123 280E
75 W114 280