Roundup all the leaves you can. Poison oak usually requires another application, so leave the vine so you can find it again. The more leaves you spray, the better chance you have of getting all of it.
By llpensinger from Ocean City, MD
This page contains the following solutions.
I know what NOT to do. Don't try to burn it. I had a friend try this and she got very sick from inhaling the fumes. I suggest wearing disposable gloves so the oil isn't transferred to anything else.
When trying to eradicate noxious weeds and vines, it may require special methods or products to do this without contaminating the soil. This is a page about killing poison oak without damaging the soil.