Poison Oak is, in fact, not related to Oak trees, nor is it a tree. It is one of the two shrubs in the Genus Toxicodendron - the Atlantic poison oak (Toxicodendron pubescens) and the Pacific poison oak (Toxicodendron diversilobum). Both species occur in North America, one in the South Eastern United States and the latter in Western North America. Both have leaves superficially resembling those of some oak trees, leading to the name.
In the Franchise, Poison Oak is incorrectly portrayed. It is depicted as a massive tree trunk with ivy-shaped leaves having fallen onto the ground. Real poison oak in fact manifests itself in the form of long, reddish green leaves, which tend to grow in clumps close to the ground, often climbing around the trunks of trees.
As a defensive mechanism, Poison Oaks contain the oil urushiol. The oil is not a poison, but a compound that causes an allergic reaction when it contacts skin. The reaction typically manifests as a raised, itchy red rash near the area of contact. Reactions can vary in severity between individuals.
There is no function of Poison Oak in the Franchise, other than as an irritant and source of humor.
In reality, some Native American cultures used the plants medicinally for various ailments.
Poison Oak is seen in the episode, "Loyal Order of Ingerman" when Snotlout, looking at the Twins going through a thorny bush to get to the other side, thinks that he is taking the easy way around the stickle thorns. Instead, he unknowingly crawls through poison oak leaves, and breaks out in a rash. The Twins apparently view Poison Oak as more painful than thornbushes.