Glyphosate pesticides (most notably, Roundup) are supoosed to be sprayed on the leaves; plants translocate the glyphosate into the root. However, I've found that poison ivy is realtively difficult to control with glyphosate pesticide. But, glyphosate is still the go-to solution as far as over-the-counter herbicides are concerned.
Generally speaking, the products specifically "designed" for poison ivy are just highly concentrated glyphosate (30%-50%). Those products usually instruct the user to cut the vine and apply the herbicide to the area of the cut stem (the lower half, with roots in the ground).
However, the best way to deal with a large poison ivy vine is to simply cut it off as close to dirt level as it is convenient to do, and then spray regular strength (2% glyphosate) herbicide on any newly emerging sprouts (on the leaves) in the surrounding area which will emerge over the next few weeks. Also, I have found that poison ivy is more susceptible to nonanoic acid (fatty acid) herbicides than many plants. But to be fair, nonanoic acid is a defoliant, not a root killer, and mixing too much nonanoic acid will cause the leaves to die before glyphosate can translocate; but if you only use a little (about 2 oz per gallon), then it will help the glyphosate penetrate the leaf and increase the efficacy of a typical 2% glyphosate solution.
Regarding the removal of poison ivy vines... the oil (urushiol) can remain viable for many years. So use caution and care when removing old vines, and do not burn them. Urushiol can volatilize and kill you if you breath it.