I am attempting to make a wooden smokehouse and am not sure what kind of glue can be used if any.
Like Al said "what for" if you want to connect the plywood to the wooden studs use screws or nails. Now you could throw s tin on the top for he rain but other then that I wouldn't use glue.
I'm not sure why you want to glue, as others have pointed out.
Having said that there are FDA approved glues out there for indirect food contact. One is Titebond III, probably available at your local box store.
Good luck and good smoking.