The problem with poison oak and poison ivy is that they emit a substance called urushiol:
http://en.wikipedia.org/wiki/Urushiol
Reactions to urushiol varies. However, mild or serious, within the first 15 minutes or so, urushiol generally binds with your skin's keratin component and cannot be washed off or removed to that degree. On the positive side, once bound, urushiol generally doesn't affect anyone else and just irritates YOUR skin layers.
Furthermore, in an actual allergic reaction, the urushiol causes skin cells to disconnect from each other. A serious exposure means that the urushiol will do this to underlying skin layers, and will soon enough cause enough dissociation amongst cells that your serum or lymph will start to leak out of your skin.
In rather serious cases (which I had, hence why I know all this), the skin will be so badly compromised that lymph will leak constantly, requiring you to bandage the area and change the bandage frequently as it soaks. Since skin is supposed to be a defense against bacteriological intrusion, you're vulnerable to infection, which is moderated slightly by the outflow. Your body hair in such strongly affected areas may fall out entirely, and the skin will resemble wax or plastic. It may be washed freely without risk or discomfort, and considering the leaking fluid and bandages, washing is a good idea.
Cortisone treatments are fairly necessary in severe reactions, since the skin needs assistance to replace the damage keratin. However, if you're OK with leaking skin and possible infections, you can forego the cortisone treatments. Eventually, the skin will heal the many millions of tiny disconnections, and the tone of the skin will improve, and the body hair will return. In bad cases, that all may not happen for 6 months.