That be some nasty looking poison oak...
Dunno how you got that from the photo. Looks like classic poison ivy, to me.
I had never gotten poison ivy in my entire life, until age 38. Then I spent a long weekend in the back yard of our new house, doing various chores... fertilizing, mulching, pulling down vines, cleaning up yard waste (and burning all of it). I never paid much attention to what PI might be or not, as I thought I was immune to it.
I got the worst case of PI I've ever seen (some photos were posted here), which lasted me about 4 months (I seem to have experienced some secondary skin rashes and infections... not uncommon with severe cases of PI). I learned a lot about PI, very fast.
I've since eradicated our entire property of PI, as well as the majority of our neighboring properties. This mostly consisted of vines varying 2" to 5" in diameter, combined with miles of ground cover PI around the perimeter of the woods. I had three weapons in my arsenal:
1. February: Double-bit axe. Walk thru the woods and cut every vine I could find. These were the big hair tree-climbers you showed in your photo. Usually two cuts, one very close to ground level, and a second a foot or two higher. Pry the vine away from the tree, leaving a nice gap between the vine still on the tree and the root in the ground, so you can watch them for re-growth over the coming years.
2. August: Tank sprayer (mine is 50 gallons, and has a 12V pump, shoots 50 - 60 feet) with wand, to spray every bit of ground cover PI I could spot, usually only a problem on the perimeter between lawn and woods. There's usually not much ground cover PI deep in the woods. Chemical of choice: Escalade, Surge, or whatever ivy/weed control I was already spraying on the lawn.
3. Any time during summer: Triclopyr, painted full-strength directly onto vines (root side) after cutting, with a throw-away paint brush. Round up (glyphosphate) is NOT effective against PI. Triclopyr is vastly superior in killing healthy / established PI. You can't really spray it full strength (will kill everything in sight, and it's too expensive to spray, anyway), and spraying diluted will often just wilt PI (but not kill it). Put it in a cup, and literally paint the vine with a brush.