Can you post clearer pictures? I'm not sure which of the plants you are referring to and the ones in the foreground are too blurry to be sure of the id. Whatever it is boiling water or vinegar won't eradicate a tough perennial weed since they don't destroy the entire root system.

Thank you for replying. Here are other photos.

Have you considered just pulling it out while wearing heavy duty gloves?

Do I see spines on that vine?

I see them!! Not poison ivy but some sort of bramble, Rubus species. Just pull or dig them out.

Thank you for all your replies! Yes, rhizo, there are thorns. I was just told in the rose forum that they are blackberry. I am glad that they are not poison ivy :)

So on second thought, I think that I will just let them be. :)

I do not recommend letting them be. Although 'blackberry' sounds nice and tasty brambles can and will form impenetrable thorny thickets covering a huge area and many feet high. The canes of some species can grow twenty feet in a season. Nothing will grow through them. This is not a plant you want in a garden. If you do wish to grow blackberries buy a named cultivar and keep it trained through regular and correct pruning.

The wild blackberries do look a lot like poison oak, and sometimes they grow jumbled up together in the wild for a double shot of evil. (If you're in CA, we don't really have poison ivy, just poison oak.)

Floral UK was too kind in her description of wild berries. They are much worse. :)