I have 4 acres of trees. Many covered by a thick combination of multiflora and poison ivy. I remember standing under a good sized 'tree' about 20' tall, with a very uniformly shaped canopy, and strange glossy leaves the size of my palm. a poison ivy vine had wound its way around the original tree, killed it, and took it over so well that it looked like a specimen tree all by itself.
Poison ivy is notoriously tough to kill and get rid of. You can't burn it. Cutting it down usually commits you to a week or two of itchy misery (and NEVER use a chainsaw on it...the chips can be murder). Cutting it without killing the roots just causes it to spread. Cutting it and burying it does the same. Never use a woodchipper (see 'chainsaw', above). I say this from experience.
There are two methods that work:
1) get a goat (great for the smaller stuff),
2) "Disconnect" the main vines from the roots. Carefully remove a 2" or so section (so it doesn't heal and grow back). Paint the lower cut with the nastiest brush killer you can find, Wait a year or two for the top to dry out, get brittle and fall off. Best to do this in the fall when the plant is sending nutrients down to the roots.
Multiflora?...toothbar... curled down...back the tractor up,...rake it into a pile...add kerosene and a match.