I just started thinking about the beasts the other day and so far i have this:
Air avatar: flying bison, you cant argue that one
Fire avatar: that dragon think Roku rides, once again aang called it roku's spirit beast so i'd say this one is fact to (can anyone tell me what the sun spirit's physical form is)
Earth avatar: the badger moles, i'll get to the thinking that led me to this.
Water avatar: no clue, but i'd guess some kind of seacreature, maybe a giant coy.
Following the theory that airbenders learned from flying bison, it would make since that their are more badger moles, in the world (remember all the bison in one of aangs flashbacks?) So i'd say that the earth benders ride the badger moles and travel through the earth. Of course, im not really sure. Also, once again i'd like to know what physical form the sun spirit takes in asian legends(particualarly chinese ones)