NEVER burn poison ivy, poison oak or poison sumac. Heat vaporizes the oil (urushiol) causing the allergic reaction and you inhale it. The vapor condenses in your lungs and the allergic reaction constricts the air passages as the mucose membranes blister, swell and ooze fluid. The allergic reaction can begin hours or days following breathing the vapor. The effect is similar to having pneumonia and asthma at the same time.
Urushiol does not break down over time. It remains in the old vines and leaves indefinately, as well on your tools unless you clean them.