Sewer Gas is from your toilet 'system'. The dryer and furnace better NOT be hooked into the toilet venting system!!! (Good GRIEF!!!)
Are you sure that your dryer ducts/piping isn't clogged??! Have it inspected along with the furnace venting. Also, check OUTSIDE where the vents terminate. If you have bushes or 'stuff' blocking or preventing the exhaust from leaving the duct, the exhaust could quite EASILY be backing up into the house. Seriously - CHeck the duct work for BOTH appliances!
Also, it's possible that the INTAKE of either system is drawing in something that 'died'. Look for intake vents and be sure that there isn't a dead animal (like a mouse) or 'droppings' sitting right in front of the intakes.
If you're having an Inspector or Service Tech doing all this 'looking around', please share my thoughts w/him/her. My best to ya and hope this helps.