You have very limited control. There are options but even though I have used maya from version 2.0 I only know of one way to get absolute control of ALL the axis (translate, rotate, and scale).

You have to use a parenting trick.

1. create an object say a pcube
2. orient it the way you want the axis
3. parent the target object to the pcube
4. with the target object selected freeze its transforms
5. make sure you are in object axis mode (hold the w-key and press the lmb a menu will pop up and check the object axis box or double click the move widget icon on the lhs of the gui and select object mode).

The targets object axis will now match the local axis - which is the parent cubes object axis. lol yeah I know wtf - object axis, local axis, world axis, axis of evil?!?! Maya's axis control system is really convoluted.

In any event you can now unparent the target object and delete the pcube and the target objects object axis will now be set to the way you oriented the pcube.

I have used Maya since version 2.0 and this is one of the primary reasons I am seriously considering switching to Modo. It can be frustrating and I can easily go on a 40 minute rant about Maya's woefully inadequate axis control system.

Note. From version 8.5 (I think) they did add a way to set the axis to a face, edge, or point. Hold down the w-key and then press the lmb, in the popup menu select axis, then "to face", "to edge" or "to point". The downside here (and again in my oppinion a serious design flaw in maya) is that it only affects the translate axis! If you pick rotate or more annoyingly scale the axis will pop back your axis setting usually object or world.

Hope this helps and good luck.