You cannot mix solid fuel (wood) combustion exhaust gasses with oil or natural gas appliances exhaust. Each type of fuel must be vented into a separate flue inside a single chimney or two separate chimneys (Oil and Gas appliance venting into a single chimney flue is OK).
Another issue is venting two wood stoves into a single chimney flue; A solid-fuel-burning appliance or fireplace shall not connect to a chimney passageway venting another appliance.
This means one stove (fireplace) per chimney or per flue. It's too difficult to control draft with multiple wood burning appliances connected to a single flue, and it is dangerous!