I don't know how much story progress you've made, but if you're still eligible to be invited to the Novice Network, Odin is pretty regularly called in there (speaking from experience as a mentor on Siren). Failing that, the Party Finder is a good tool for this, as suggested above, or you could try to find a good hunt Linkshell to be invited to, as most of them will also call/participate in things like special FATEs.

In fact, you can feel free to shoot me a /tell in game and I'll invite you to the NN (if possible) and the hunt Linkshell I'm in if you'd like. Just remind me that you're the guy who was asking about Odin on the forums, haha. Otherwise, best of luck! I'm sure you'll get those mantles before too long if you keep working at them.