This is the working or itching part of poised oak / ivy. http://en.m.wikipedia.org/wiki/Urushiol#section_1
It says you have a ten minute or less time frame to wash it off.
But as far as the oil still being on the camp stove? Up to five years as this link will verify. Cool also about the Japanese method for protecting their gold leaf.
http://poisonivy.aesir.com/view/fastfacts.html
My wife picked up some at Cleburne state park when geocaching the first of the month. Don't laugh but an old cure I learned while in the Army, Niagara Heavy spray starch. Don't know how or why but it works, stops the itch the minute it hits the rash. Crazy? But it works.
Tim