Answers

I also like the goat idea. We used to raise them, and they will indeed eat anything they can ingest, so you have to be careful about not only what you want to keep, but any potentially dangerous or poisonous plants in the area.

On the chemical side, a quality broadleaf herbacide or roundup should kill it. At least for the season.

The best way to remove the poison ivy would be to get a goat or two. A pair of goats would have the poison ivy in about a day without leaving any chemicals left behind. Keep in mind though that goats will also eat landscaping if you have it. There are different chemicals and techniques to revmoving the poison ivy if you don't want to go the goat route. Keep in mind that if you choose to use chemicals be very careful and be sure to chang clothes frequently through this process and wash your skin a lot. 

Awesome answer.  Goat are machines and they do have rental goats.  You will need to keep them penned up where you need them though or they will clear you out.