Outsiders are living creatures, so they can heal naturally. Even though they don't need to sleep. However, they still must rest for 8 hours (just like a spellcaster who does not need to sleep.)
Most Outsiders can choose to sleep (just like they can eat and drink) even though they don't have to. Thy can also read, relax, meditate, or engage in any other restful, non-productive behavior.