I just grab it with my bare hands and dispose of it. It only barely affects me. Although I did tangle with a vine about 2" in diameter earlier this year that gave me a lashing and a half. I still won that battle.
I'm so allergic to the stuff, I break out just looking at it! And of course, hubby is totally immune. He pulls it up and weedeats it with impunity, then I wind up with a rash when I do laundry. I finally learned to wash his clothes separately, and to wear rubber gloves when handling his clothes.
Poison Ivy isn't hard to kill. I pull it up (gloved, of course) or spray it. Any product with glyphosate or triclopyr should be effective, though you may need to retreat (and be careful not to get the spray on desirable plants, or they may be killed as well).