Will get a professional in here ASAPby code you cannot run a wood stove and an oil furnace through the same flue. So yes the wood stove needs to go or be hooked up correctly to it's own flue.
They will look at everything and give you options on how best to make it safe. from the limited pics i see your setup is far from safe.
Anything that can burn. All of that wood i see in that pic needs to be 18" minimum from that pipe. The stove will need 36" minimum to anything combustible.
As it is it can not be used safely. You need someone to come there and look at the whole situation and see what options you have. But honestly from what i can see so far i don't think that either the wood stove or the furnace are safe to use