Welcome to Just Answer.
The toilet or main drain pipe can be partially clogged or the main vent pipe can be partially clogged from an animal getting caught or a bird building a nest, etc. You should try snaking both with a plumbers snake, to clear any blockages.
A high pressure nozzle, on the end of a water hose, can be used up on the roof to spray down the main vent pipe. This is effective at clearing blockages in the vent pipe only. Watch the short video below, to learn more about plumbing vents and how to clear them.
As far as the sewer smell after turning on the air conditioner goes, it is most likely one of the following:
The air conditioner is simply moving air around and making the problem more noticeable; when the A/C is off, the problem is still there, just not as noticeable. The first thing to do, is to really try and narrow down where the strongest smell is and where it is coming from; do this when the A/C is first turned on. This will help tremendously and once this is established, the things discussed earlier can be used to further find and ultimately fix the smell problem.
If you need further help or clarification on this answer, please reply to this post.
Best of Luck, Brian
This is the perfect clue!
I can guarantee that if you inspect the bathroom that is closest to the return air grille, that you will find the smell problem.
I have seen this time and again, because the return air grille is sucking air to the furnace/ air conditioning and re-distributing that air throughout the house floor vents. Just to test it, try spraying some non-flammable air freshener near the return air grille......within a few minutes the whole house will smell nice.
So back to the inspecting......the nearest bathroom needs to have the traps filled with water by running the faucets and gently wiggle the toilet to see if it moves. If the toilet moves, it is a good sign that the wax seal is leaking sewer gases and needs to be replaced. Replace the seal and the smell will be gone.