I have a similar problem. My 2006 E350 station wagon with 23,000 miles has a greasy odor problem that occurs only after a rain or carwash, but not immediately. The car must stand with the windows up about 3 hours after it has gotten wet.

I have tried to isolate the problem by hosing water, one section at a time; first on the front section of the car, then the middle section of the car, and then the rear section of the car.

I determined that the odor only manifests when the middle of the car is soaked and the car sits for a few hours with the windows up. The motor does not need to be running and the A/C does not have to be on. The dealer cannot find the source of the problem, tried to fix it by thoroughly cleaning the A/C system

After airing out the car, I smelled areas around the doors and as a result suspect that the smell originates in the window wells on each of the 4 doors.

 

I have a very similar problem with my 2006 E350 wagon after a rain or car wash. Not right away, but after the car sits a few hours the cabin smells like grease (not gas or mould). It is driving me nuts trying to find the source and the dealer, though trying to help is perplexed.