For buttons like the MENU or BACK button you can just add a listener for KeyboardEvent and check if the event keyCode is Keyboard.BACK or Keyboard.MENU.
However I don't see anything for knowing if the phone's volume buttons were pressed.
Is there a way to listen for volume up and volume down keyUp/keyDown events in AIR (ActionScript 3)?
Nope. There isn't any support for detecting the volume buttons. (In AIR 3, you can write a native extension to access native features that aren't otherwise supported.)