A leaking wax ring can allow gas to leak. These are cheap, and though messy to replace, something you can probably do yourself. That may not be the problem, but it is cheap to check. You could have a broken joint or a hole in your vent stack, but this is not common, either. Is it plastic or metal? A leaking vent will let sewer gas escape, but will not cause the toilets to back up. If all of the toilets in the house don't flush, how about the washing machine (if you have one), does it cause problems, too? It is probably the biggest waste volume while running in the house.
Still sounds to me like you have an obstruction in your line. It could be anywhere between the house and the city's main sewer line out by the road. You could also have a broken or collapsed line. Has there been any construction on your property recently? Has a big truck been through there? Any digging, backfilling, etc? These lines are often down a ways, so that usually doesn't affect them, but a heavy construction vehicle, depending on the pipe and where it is, can cause problems. Do you have trees in the yard near where the sewer line goes? If there is a gap or crack in the line, roots can get into the line and really mess things up.
You can rent the tools to try to clean out a sewer line, but it is messy work and takes some knowledge of plumbing. You might create more damage than you solve if you don't know what you are doing. If you have a cleanout in the basement where the line goes out to the street, if you don't have an obstruction in the house, you'd be pretty safe trying to see if there was one between the house and street. It is sometimes a bear getting the caps off of these things, though. Sometimes, you end up breaking the thing and having to put in a new one.
One of the pros will have some other ideas, but it seems to me thatyou need to check for an obstruction anywhere between the house and the street. If all of the toilets in the house are doing the same thing, and they worked correctly previously, it has to be common to all of them - the main line. Find the toilet closest to where it meets the line going out to the street, and check from there out. If the washing machine doesn't back up things, then it seems like it is probably between that last toilet and the washing machine (this assumes thatthe washing machine is in the basement, which may not be valid).
The sewer gas seems like a second problem, maybe unrelated to the flushing problem with the toilets.