This question may seem like an impossible challenge. What I'm talking about here is a biological explanation for limited (or, for bonus marks, unlimited) form shifting, immortality (at least in age) and the ability to defy physics.
For example, in Ribbontail's series Aman5 she has a complex system of gods that are nothing more than extremely powerful aliens that live off of planets; this includes everyone's favorite god: Eclipse.
You can go as far off of Earth biology as need be as long as it is believable. Bonus points if you can explain omnipresence, telepathy or reincarnation, although these are in no way necessary.
They don't have to be gods, per se. For example, if I went back in time 10,000 years with a hummer and a machine gun (or even a musket), I would be seen as a god. Scale this up and even an advanced culture could see an alien as a god.
A list of all of the Anatomically Correct questions can be found here