Personally I'd check the vent pipe first for any blockage, which would cause sewer gas to vent back into the house instead of outside.

Is your dryer vent clogged or maybe harboring a dead animal? Worth checking.

When operating your dryer, your actually creating a negative pressure on your house. All the air it pushes out has to be replaced from somewhere. If you had a dead animal in a fireplace chimney or furnace flue pipe it could be pulling air over the animal into your house.
Mike