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It is possible that this "weed" may have been poison ivy or oak. Or within that family as its sap, which was dripping from the plant, is what normally causes rashes to occur. While many people think of them as only small, 3-leafed plants, they will actually produce large, woody vines that can climb throughout surrounding trees and structures. This article will help determine if this is in fact your weed: https://www.gardeningknowhow.com/special/starting/poison-ivy-control.htm

If you do not feel this is the weed in question, feel free to send us a picture and we will help to identify it for you. Send to: questions@gardeningknowhow.com

The poison remains active even after the plant is dead. If you're looking to get rid of poison ivy (or oak), treat with herbicide first (to kill the roots) then, wearing gloves, hand pull dead plant material and dispose of it. Do not burn it, however, as the poison can be breathed in and will result in a nasty rash. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/weeds/poison-ivy-control.htm

I assume that you mean you will remove a PO vine that has been growing up into a tree, and you want to remove the PO oil residue from the tree stem and/or leaf surfaces in order to avoid exposure to the oil when working with or climbing the tree.

I can't think of any way to effectively remove all the oil residue, only specialized soaps/solvents can remove the tenacious oils from human skin even in the best of circumstances. Ordinary soaps and detergents may remove the bulk of the oils, but a person whom is highly sensitive to poison oak may still be exposed and get a reaction. Maybe insecticidal soap sprayed on and then washed off will get some of it, but I don't think it will get all. Time and weathering will dilute and biodegrade the oils and reduce chance of exposure. But give it a year or two if you are highly sensitive to poison oak.
If it were me, and I really needed to go into the tree after the PO was removed, I would concentrate on washing my exposed body parts as soon as possible after exposure with Tecnu soap. Follow the directions explicitly, don't shortcut the recommended procedure. It works.