I heard this solution on the French radio. It was given by the chief gardener of the Versailles palace in France. It works to get rid of vines like bindweed using strong systemic herbicide but without damaging the soil or other plants. I think it should work on poison oak. I will try to explain what you should do, but I also made a picture (very badly drawn!) to make it more clear.
You need two plastic bottles: a big one, and a smaller one that fits inside the bigger one. Cut off the top third of the two bottles.
In the bottom part and the top part of the bottles, make two holes (about .2 inches wide) one on each side of the bottle at about 1.5 inches from the edge. You can make the holes using the tip of a screwdriver or a knife pre-heated on a flame. With a pair of scissors, cut the plastic from the edge to the center of the holes.
Protect yourself; use gloves, disposable suit, you can even cover your face and wear protection glasses as what you have to do doesn't require precision. Get a stone that can fit in the bottom of the little bottle. It mustn't be too big. It just has to stay stuck at the bottom of the bottle without damaging it, of course.
Hold a part of the poison oak that can bend, if possible, not too far from its roots. Bend it, and get it inside the little bottle right to the bottom. Put the stone on top of it so that it will hold the plant down at the bottom of the bottle. Slide each end of the plant into the cut you made in the bottle down to the holes.
Pour a systemic herbicide (like Roundup for example) into the bottle up to the holes. The plant has to be submerged and the herbicide has to be systemic. Put back the top of the bottle on its bottom part getting the holes one in front of the other. Secure with tape from lid to bottom if needed. Put the little bottle inside the bigger one slide down each part of the plant into the holes put back the top part of the bigger bottle and secure with tape.
The systemic herbicide will work its way up through the plant system, and down to its roots. The herbicide will not enter the soil and only the vine will be killed. The bigger bottle is used to avoid any spilling of the herbicide from the little one, and to avoid animals drinking or being intoxicated by the chemical. You should dig a little hole large enough to secure the bottom of the bigger bottle or set stones around it to keep it steady.
Once the plant is dead you, just cut the parts that stick out of the bottle and you can reuse the bottle for another plant. The herbicide will still be strong enough.
You can accomplish the same thing by using an old paintbrush and "painting" the herbicide on the plants' foliage. I save the paintbrush, in a small plastic bag, for the next plant I want to get rid of.