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It's hearsay, but a friend of a friend cooked something on skewers of either poison oak or poison ivy (I don’t remember which), and suffered for it. I don't think you want to get near the smoke when either of them are burning, let alone let them near your food.

That's actually true.

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DO NOT burn poison ivy, oak, or sumac to get rid of it. The resins can be spread via smoke, and can cause severe reactions in people who are far downwind.
-- http://www.nlm.nih.gov/MEDLINEPLUS/ency/article/000027.htm

My comment about not using evergreen woods for food preparation is just paranoia perhaps, but it's so easy to avoid... *shrug*