I'm a little confused by your request, but I think you're asking how to change the orientation (and/or location) of the object's axes relative to its shape. In Anim8or terms, that means "change the object's pivot point."
This can be done by selecting the "edit pivot point" mode. It has operations similar to those available in the "edit object" mode.
In the screengrab below, I moved the object away from the origin so that the pivot point's axes can seen more easily. They're hard to see when they overlap the "World" axes, as they do when the object is centered. I've also rotated the pivot point somewhat.
The "Edit" menu in the top row of options has a "Pivot..." entry which provides a few edit options, too.