Poison oak isn't found in Michigan. It looks very much like poison ivy, and they are related. So, unless someone brought some up from a southerly location you shouldn't come across it here. You will want to be aware of it if traveling to locations that have it, of course.
The USDA Plants Database lists 'poison oak' as the common name covering all Toxicodendron species. But what we commonly call poison oak- Toxicodendron pubscens' doesn't grow in Michigan-- see the following maps for where each species of Toxicodendron grows---
Here are some references on rash-causing weeds with pictures. Please note that 'poisonwood' is not found in Michigan, either. But the Florida Extension article has a good description of poison ivy and poison sumac:
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