This sounds like two distinct problems: you have an exhaust leak and you have a way for that exhaust to get into the cabin...

I'm not very familiar with your chassis, but on my w123 the battery sits in the right rear corner of the engine bay, near the heater box, and somewhat above the exhaust manifold. If yours is in a similar location, (or even if it's not) you might consider pulling your battery & tray to inspect for a hole in the firewall (rust likes to form under & around batteries). If you find one, let me know and I can provide some suggestions on how to patch it without welding if you'd like.

As far as where you have an exhaust leak, you might try holding a piece of tissue around the exhaust flanges & fittings with the engine running (be safe, use common sense, etc) - if the tissue starts blowing around, that's a likely leak.