How to reset pivot point? I have multiple objects in my blender project, but the origin is faulty for all of them.

I would like the origin for each object to be at the center (geometry, or mass), but even if I select that for each of them, one by one, it does not appear to work.

It appears that my XYZ axis are at the cursor, rather than at the origin of the object. How do I change that?

(Feel free to edit question if unclear, incorrectly worded, or addressing something other than the origin point. I'd like my XYZ axis to be at the center of mess/geometry for each object automatically. This was originally so, but I did something to mess it up.)

Blend file: http://pasteall.org/blend/index.php?id=47595


UPDATE: It appears that, in addition to the "origin point" issue, my 3D cursor was set to "Bounding Box" rather than "Median Point". Thank you all!
First of all you need to change Pivot Center to Median Point from 3D cursor, and secondly you still have some parts that needs Ctrl+Alt+Shift+C > Origin to Center of Mass. Mostly on handle.