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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:
can come up thru a sink drain if the trap below the sink is not full of water. Using the sink regularly is what keeps the trap full of water. If the sink is not used often enough, the water in the trap can evaporate, allowing sewer gases to flow past it. Often, if there is a problem with the plumbing vent, such as a partial blockage, or the vent is installed incorrectly, the water can actually be siphoned out of the trap, allowing the sewer gas to escape. If the smell is recent and the sink has been in place for a long time, then it would be safe to say that the vent was installed properly. I would go around your house and run the water at each sink, shower and tub for 10-20 seconds to make sure all traps are full
The smell could be coming from the wax seal located at the base of any of your toilets, in which you would just have to remove the toilet and replace with a new wax seal.
Highly unlikely, but it could be coming from a loosened/ disconnected joint in the vent system, in the wall. Unfortunately these are not easy to find without removing the portion of wall where the fixture drain enters the wall. Before doing this I would check all visible joints, between the trap and the wall, and then see if the odor is strong where the pipe enters the wall. This would be a sign of a loose joint behind the wall.
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