Plumbing – We just bought a house and the guest bathroom has an awful smell coming from the toilet, how can we figure this out

The two most common sources I've seen are dried out traps and a failing wax seal under the toilet. A failing wax seal may also result in water damage appearing from beneath the toilet. The dried out traps are simple to fix, just run a little water into each drain every few months.

For a, more rare, problem at a PVC joint, you'll need to find the offending joint first. Look for signs of water damage, or you may get lucky putting some soapy water over each joint and flushing a toilet.

Edit: here's a good description of how to replace the wax seal under the toilet: How do I fix a leaky toilet that only leaks from underneath?

The overflow pipe is for when the tank is full AND the normal fill-control system for the tank fails. If there is water entering the overflow pipe either due to a failed fill control setup or due to a leak in the connections at the bottom of the tank then that is a problem that should be fixed.

I would suggest adding some food coloring or similar dye into the tank. This should allow you to quickly determine if the water is coming from the tank or not.