The axis for all of my object manipulations seem crooked.
This is a known bug. I have reported this many times. No fixes yet. It happens after you applied deltas to animated keyframes. Then your axis will not respond to normals, world, local or anything else.
The only solution here is to extract faces of the mesh with P (part them) and then reconstruct them again by "Join" J
Then you will have your pivot point again in a fixed correlational position with the other joined elements.