Perform action on logout,
Even adding something as simple as drupal_set_message doesn't result in a message being displayed.


That's the  expected behaviour - in the logout hook, you're still inside the authenticated user's session. Once they're logged out, you're not any more. So messages intended for that user are no longer there, because that session has been destroyed.

You should implement a logout/token expiry resource in your API, and invoke that in the logout hook. Then you don't need to remove the token held in local storage, as it will not be valid any more.