I asked this elsewhere and decided to bring it to a more "formal" questions space. I couldn't find more direct answer for this.
The animal companions from each of the above classes (Cavalier/Samurai, Life Oracle and Mammoth Rider) stack provided they all share an animal, correct? For instance, a wolf is on all the lists (for a small creature). On the other hand, I couldn't have a baluchitherium or triceratops as my companion because it is not on all the lists.
Additionally, if I were to have enough levels to get to Mammoth Rider (8 Cavalier, 1 Oracle (Bonded Mount), 1 Mammoth Rider), can I get a Huge wolf? As a halfling, can I actually ride this mount?
Finally, in the above example, would my mount have an int of at least 6 from Bonded Mount?
You are correct. As long as the animal is on all of their lists, they will all stack. As long as it is as least 1 size higher than you, you can ride it, so you can ride a huge wolf, or colossal if you increase its size magically. It will indeed have the increased int from the Oracle revelation.
Thank you kindly, Wiggles: I greatly appreciate you helping getting this cleared up for me.