Even though you sort of tested it you must have an Exhaust leak somewhere.

You also did not say if this was while the Car was moving or only when the Car idled.

Do you have any sort of tial pipe Smoke; and if so what color is it?

Side note:
I had occasion to drive my Car without the Crankcase Breather Hose connected. Not only did it get stinky fast but at idle vapor came out from under the hood.
So 2 things. It might not be Exhaust and if there is a leak it might be under the Hood.

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84 300D, 82 Volvo 244Gl Diesel