The part that relates to the sword is the part that is a little more difficult to wrap our heads around (given that it has, apparently, been running around by itself, possessing bodies for the sake of killing stuff). The easiest way to explain the sword is to simply say that it is a Primal. After all, it can temper (or possess) people, it can cut pretty much anything, and it has a will of its own... sort of... a mix of wills between Odin and it, would be my bet. It is this mix, though, that makes me think the Sword might have a different connection to the Lore of the game.

For one, every weapon in the game has a means of becoming attuned to it's wielder. The system has been in place since forever. Spirit bonding. It could be that Zantetsuken is simply a supremely powerful sword that has been completely Spirit Bonded to Odin. For this reason, whenever it gets a new body, it fashions that body to Odin's likeness and will because of the bond they share. A Spirit bonded weapon cannot be used by another person. No matter who the sword possesses, it has to turn them into Odin.

Another interesting, and disturbing, thought is that Zantetsuken was forged the same way the Zodiac Zeta Weapons were forged. It has already been established in the lore that the original relic weapons from back in the day could never have been used by anyone other than their original owners because they had developed a sense of consciousness. They had a will. The Zeta questline had us reproduce the result by distinctly forging each section of the weapon's consciousness using mahatma. They became more than just weapons. They, supposedly, had minds of their own.

It could be that our Zeta weapons are one step shy of being exactly like Zentetsuken, or that the original zodiac weapons of eld (if they are still out there somewhere) could be like Zentetsuken... Or that Zentetsuken is one of the original Zodiac weapons. Given that we don't know the origin of the blade, or who used it first (as we know it was not Odin's originally), it is entirely possible that Zentetsuken is a Zodiac Weapon of the original Zodiac Braves, which may have lore implications for any future Relic Quests, if they make a new relic.