Hi, 

If the poison ivy isn't in an area that will both you, you can leave it. It is a native plant and doesn't harm the trees or wildlife. Birds, squirrels, chipmunks etc will eat the berries. It can actually be quite beautiful in the fall when it turns shades of bright red and orange. 

If it is growing in an area where you will come in contact with it regularly and can't avoid touching it then you can either cut or pull it up from the roots, or carefully apply a systemic herbicide to the leaves or cut vines. You can let it hang on the trees and it will eventually fall out as the vines die. That way you don't risk breaking any branches trying to pull it down. 

Usually if it is on trees it isn't bothering us, it is more so if it is on the edge of lawns or entwined in a garden bed that we access. If you can just watch out for it and avoid it, then it has its place in nature!

Here is some further information on Poison Ivy

Emily