First things first; this class is very interesting, and rather original. I like it.

But criticism is more useful than praise, so I'm going to be critical. This class is powerful. Not "broken tricks no one would actually use in a game" powerful, but "wow, Angela, leave some enemies for the rest of us" powerful. You have a damage output that would make a Warlock throw itself off a building, significantly better healing than a Dragon Shaman or Bard, and enough good defensive abilities to make any mundane martial class look like an Elf with 6 Con.

Now, granted, you don't get everything at once; but each of the three tracks of this class has all the power and versatility of a Tier 4, and you get access to all three, every day. You can switch between encounters, or just focus on one that suits you and use the others as emergency backup.

Your healing, in particular, is extremely powerful because you can Rezz people with no real cost. Assuming the ability is Su, you have unlimited free Resurrections at high levels. Now, granted, a Resurrection never hurt anything, but when your party has no fear of death the game gets harder for the DM. Why fear losing your life to the dragon when your buddy can bring you back for free?

I have a hard time judging the Tier of this class because it's really three classes, tied together. They're tied together in a decently flavorful way, but the matter still stands that each Avatar plays very differently, to the point where they have different BAB's and proficiencies. It almost seems like you're forced to pick which one you're using; if you go Dragonkin, for example, you have to put money into a set of Mithral Full Plate and a martial weapon that you can't use in your other two forms.

So, yeah. I'm not sure how to best convey it, but this class seems exceptionally versatile and strong. A very well-run Sorcerer or Psion is stronger, but they also have limits per-day; this class doesn't. I'd play a Legendary Ascendant, but I feel that I might have to tone it down to avoid overshadowing other party members.