Poison ivy, oak, and sumac can be very hard to get rid of. You have three choices: removal by hand, use of an herbicide, or suffocation.
Interestingly, these are native plants, and therefore considered desirable by many environmentalists. By native, I mean they and the local ecosystem are well adapted to each other and support each other. Removing these plants altogether from the region would actually disturb the ecosystem and limit biodiversity! That said, I too am highly allergic to these plants and will not tolerate them around my property. Let them have the woods, but please, not in my back yard!
Although I'm highly allergic, I physically remove poison ivy from my property. I do this in winter or summer, the two seasons when the plants are least virulent. Be sure to remove the whole plant, including the roots. Of course, covering your skin will help a lot. Wear long pants, a long-sleeved shirt, elbow-length gloves, and possibly a bandanna over your nose and mouth. When you're done, immediately remove all these items, wash them, and wash your arms and face thoroughly with Tecnu (a great product for preventing an allergic reaction). These plants are at their strongest in spring and fall, so avoid them completely in these seasons. (You can hire one of the non-allergic elite to remove poison ivy and sumac for you, but studies show that repeated exposure will lead to the development of the allergy over time, so you are not doing these folks a favor.)
Most herbicides are designed and proven to break down within 24 hours of exposure to light and air, the downside being that they kill not only plants, but also live soil bacteria. If an herbicide like Roundup or Brush-B-Gon is applied selectively, the environmental damage is minimal. Be careful to avoid getting herbicide on the soil or surrounding plants. This is a tradeoff, 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. Personally, I believe that careful, selective use of herbicides is a tolerable risk. In my mind, herbicides?which kill the plant through the root zone?are more reliable than mechanical removal. If you don't get all the roots, the plant comes back and you 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 (rich in live microbial cultures) into your soil on a regular basis, you will counteract any damage that a very limited quantity of herbicide might do to your topsoil. Do keep in mind that applying these products to large areas will result in "dead" soil that will take at least a year to rejuvenate.
Last of all, there's the pond-liner solution. Get some heavy EPDM pond liner and put it on top of the plants for three to four weeks in active seasons, or for as long as seven weeks in the winter. This will suffocate the poisonous plants (and any other plants under the pond liner). It also suffocates the soil?with the same repercussions to topsoil as herbicides?since the pond liner prevents moisture and gas exchange vital to microorganisms. Any thickness of pond liner will do the trick; however, the heavier the pond liner, the more durable it will be and the more you will be able to reuse it.
One final word of warning: NEVER BURN THESE PLANTS. Inhaling the fumes will cause dangerous allergic reactions in unimaginable places!