Yes, I have the vines as well, and they grow like crazy!
They do make a brush killer labeled for poison ivy, but I've had good luck doing the following:
I cut the vine a foot or two from the last root. I take a small container of full strength roundup, and dip the cut end of the vine (the part that is still rooted in the ground) into the pure roundup and leave it for several minutes. (when I'm working with the ivy I wear protective clothes, gloves, and eye protection.)
This usually kills the vine within a week or two. It's a pain to do a bunch of vines, but it works. I've thought about an alternate method, but haven't tried it yet. Cut the vines as above. take a cotton ball and dip it into full strength roundup. Place on the end of the vine, and cover with a piece of aluminum foil crumpled to hold it on the vine. With this method, you could do a whole bunch without taking the time to soak each vine. If you try this, be sure to collect the foil pieces and cotton balls and dispose of properly.
While we're on the subject, a company called Gemplers
Insert usual disclaimers.
HTH,
Paul