The answer is going to be state specific, so checking with an attorney is probably the best answer. But, most states have fairly similar rules. The owner is not supposed to remove any fixtures (furnace, plumbing, sinks, etc.) In Washington state, even blinds/curtains are considered fixtures.
That doesn't stop owners from stripping the homes. Its common to see toilets or similar fixtures removed... or damaged. In some blatant cases, they may remove the furnace or even heat ducts.

Make sure the ivy you're viewing is not Virginia Creeper, which is a desirable non-poisonous vine often found in gardens in the southeast.

Ortho and Spectracide products found in your local garden center such as at Home Depot or Lowe's carries concentrate specifically made to get rid of poison ivy without you having to touch it. Wear gloves, spray on a windless day, and you should be rid of it in no more than two applications. The dead vines do still contain some poison, so if you still must pull them out, invest in a bottle of Technu, found at your local drugstore, which immediately gets rid of any poison ivy/poison sumac/poison oak oils your skin may come in contact with. I use it and it works, but my suggestion is to cut the dead vines with a pruner before removing them, and then cover the dead source of the plant with some black plastic weighted with concrete block, or heavy brick, for at least one month up to two months to kill any new ivy which might start to sprout.