The most common allergy in the US, I am told, is that to urushiol, the active ingredient in oils from these two plants. I’ve got a severe allergic reaction and have gotten it from the fur of pets and other peoples’ jackets, as well as from personal contact. There’s a preventative that has worked so-so for me, Teknu; you wash your skin, clothing, boots, whatever, with it after exposure.
But the most effective thing I have ever found with regard to poison oak is Neutrogena Body Clear Body Scrub, a skin-scrub that is designed for use against acne. I haven’t used it to prevent outbreak after exposure, but to reduce the swelling and itching once I’m broken out. DO NOT scrub hard, and don’t use very hot water, just luke-warm. Rub the stuff on liberally (gently!) and then let it sit on your skin for two or three minutes. Longer may be better, can’t hurt. Then rinse it off with luke-warm water and towel dry gently.
The active ingredient here is salicylic acid, which has a drying effect on the skin and on the poison oak blisters. It has lessened the itching and also the length of time the breakout lasts. For me it has worked very well; calamine lotion and other things that are promoted for use against poison-oak rash have helped little or not at all. (Rash, they call it! a mild term for this, with its intolerable itching, swelling, oozing!)
Salicylic acid is related to aspirin (acetylsalicylic acid) I suppose, and both are derived from willow bark. So if you had to you might try crushed aspirin made into a paste with water, or boil up some willow bark and make a poultice.
[Standard disclaimer: neither I nor anyone associated with me has any financial interest in any product mentioned here. I am growing a bunch of willows for a windbreak, easiest plants in the world to grow, but I have no plans to strip their bark for sale.]