Growing up in the woods near the coast of California, I had much intimate experience with poison oak. I had a donkey with a fondness for the stuff, and she'd selectively munch through an area, leaving all other foliage. People used to borrow her for this all the time. You can imagine. You have to have direct contact with urushiol oil to get the allergic reaction.
Urushiol oil can be active on any surface for five years and possibly longer.
I have heard that urushiol can become airborne from a lawn mower, but I've never heard of anyone actually catching it that way. You can be dangerously exposed to the toxic oil of poison ivy through the smoke when the plants are being burned. This can affect the throat and lungs, and can even be fatal. So don't burn the stuff. I would also recommend that you not touch your silly friends who are rolling around in it.