Since you didn’t describe that water heater’s (or maybe something else) “smell” scent / compared it to anything, I can’t suggest any remedies. The hole in your chimney should definitely be sealed because it might compromise proper draft but it’s difficult to say if it has anything to do with the problem you’re describing.
The odor doesn’t have to be associated (however it’s possible) with a running air conditioning unit, it might be just “amplified” because of the circulating air is pulling that smell from some area.
A water heater tank might be responsible for creating such unpleasant odor but this would be associated with running hot water faucets or having that hot water stored in some open container.
20+ year old water heater may have a significant amount of mineral deposits accumulated inside the tank which decreases the amount of hot water stored inside and sometimes significantly increases the heating time. Also, at that age of your water heater you should be prepared for its failure (cracking and leaks). I’m not saying that it’s going to happen today or tomorrow but you shouldn’t be surprised if you see some water dripping from the appliance and accumulating around its base.
Maybe you should consider water heater replacement and see if this takes care of the problem.