I have poison ivy and ticks that keep me out of the areas where I should be doing property maintenance.
I can get a poison ivy reaction just mowing on the tractor!
If you absolutely must get down in there to kill a few more trees, you can try girdling or frilling. (Or those techniques plus herbicide.)
Read up on those techniques and get your axe really sharp, and then you should be able to readily kill some of your big trees.
Girdling is usually most effective in the late spring when the trees have sent the maximum energy reserves from the roots to the treetop to grow leaves. Perhaps make a few paths through the poison ivy and briars this spring so you can safely reach your big trees. I like Crossbow for poison ivy.
(I get Crossbow herbicide pretty cheap from my county Noxious Weed Dept. That stuff is great on poison ivy and won't harm grass.)
