Poison ivy, oak and sumac can be very hard to get rid of. The three choices are mechanical remove (by hand), use of an herbicide, or suffocation .
Interestingly, these plants are native plants, and therefore considered desirable by many environmentalists. By native, I mean they and the local ecosystem are very well adapted to each other and support each other. Removing these plants altogether from the region would actually disturb the ecosystem and limit bio-diversity! (more on this on the Garden Web forum: http://forums.gardenweb.com/forums/load/natives/msg051448464442.html )That said, I myself am highly allergic to all three of these plants and will not tolerate them around my property (1/3 of an acre). Let them have the woods, but please not in my back yard.
Though highly allergic, I will physically remove poison ivy in the winter and summer when it is least virulent. Of course, covering yourself with long pants, long sleeve shirt, elbow length gloves, and possible a bandanna over your nose and mouth help a lot as well if you are allergic. Remembering to immediately removal all these accoutrements (wash them), and wash your arms and face thoroughly with Tech-Nu (a great product for preventing allergic reaction to these plants) limits the chance of an outbreak thereafter. These plants are at their strongest in higher growth periods like spring and fall, so avoid them completely in these seasons. You can hire one of the non-allergic elite to do this for you, but studies show that repeated exposure will lead to the development of the allergy over time.
Though most herbicides are designed and proven to break down within 24 hours of exposure to light and air, they not only kill plants, but also kill live soil bacteria. However, if applied selectively, on a plant by plant basis, the environmental damage is minimal as long as you avoid getting the herbicide on the soil or surrounding plants (more on this at http://www.hort.purdue.edu/ext/HO-218.pdf). This is a trade off of course, some folks are plain anti-chemical (except when it comes to termites, roaches and rodents). Other folks will stretch it to poisonous plants. For myself, I believe that careful, selective use of herbicides is a tolerable risk. In my mind, herbacides which kill the plant through the root zone, are more reliable than mechanical removal wherein if you dont get all the roots, the plant comes back and one may have risked another rash for nothing. If the plant comes back, hit it again until it does not. As long as you are working composted material into your soil on a regular basis, you will counteract any damage that a very limited quantity of round-up or brush be gone might have done.
Last of all is the pond liner solution. This works for any plant by the way. Get some heavy epdm pond liner and put it on top of the plant for three to four weeks in active seasons, or as much as seven weeks in the winter. This will suffocate the plant and anything else under the pond liner. It also suffocates the soil with the same repercussions to topsoil as herbicides.
Note: NEVER BURN THESE PLANTS. Inhaling the fumes will cause outbreak in unimaginable places!