<< This sounds to me like it could be the vent pipe. Is this a possibility? >>
Good first place to look. And cheapest to correct.
<< How do you determine if it is indeed at fault? >>
Take a hose up on the roof, put it in the vent and turn it on. If the vent
fills with water fairly quickly you.ve found the problem.
<< And how do you clean it out? >>
Try the usual tools, a plumbers snake, etc. However, the main drain may have
tree roots impeding flow. Best diagnosis there would be a pro with a drain
scope. Good luck.