Since you say polygon I assume this is 2d? Dynamic tests for combinations of OBBs, AABBs, and polygons aren't quite 'simple', but aren't too complex. The separating axis method can be used for all the tests you describe. There's an article by Gomez in gamedev->articles->collision detection that describes the algorithm for swept AABBs. The technique can be generalized for OBBs and convex polygons. See geometrictools.com->documentation for an article on the separating axis method as it applies to convex polygons and polyhedra. The method is particularly nice in 2d because there are no degenerate cases to handle.

Too bad about gamasutra - that article has a very clear explanation of the swept AABB test, with code. Perhaps Nice Coder's suggestions will help, or you could find some other way to get ahold of the article.

If you haven't already, you might give this article by Dave Eberly a try - it's a little lighter on the math than some of the others, and includes pseudocode for the algorithms described.