Here we talk a little bit about the word used to describe Odin in Japanese (闘神=TOSHIN=lit. god of fighting) and how it is similar to the Japanese term 三闘神 (SAN-TOSHIN=lit. three gods of fighting), or what is translated in the EN version as the Warring Triad. It’s here that we mention that toshin is actually just the term that the Allagans used for primals (primals being a relatively recent (in Eorzean history) term).
So Odin is named "Primal". That's all That is said here... Please give full infos when you quote your sources... Maybe he is part of the warring triad, maybe he isn't...