Is Oumuamua tumbling? given that everyone wonders whether there is a chance that there is something to oumuamua that is not natural, what about tumbling (and/or aiming?)?

is there a natural gravitational or other force that would naturally stabilize non-orbiting asteroids in space?

I would guess that there is a chance that we could detect tumbling.
Assuming that this is a serious question... yes, Oumuamua will be tumbling, just like every other small body. 

That it comes from outside the Solar System does not change that it will have three axes of rotation because it is small and thus has not accreted enough matter that it would stabilise into a single primary axis. (This doesn't preclude one of its axes being a primary spin axis.) 

And just like every other small body, if we collect enough data in the form of reflected sunlight from its surface, we can construct shape and rotation models and estimate its size and composition.