Odin will be nerfed next patch (4.17 ''The Odyssey''), which is a good thing IMO (since jgl Odin has been op lately). Anyway, he will still be viable and fun to play in Arena no doubt. Brawler's Beat Stick will also be nerfed, cost will be increase from 2200 to 2350 because it was too good on its own even if used as anti-healing or not. That's why I added Titan's Bane on Full build example 1, even though Brawler's will probably still be the best choice because obviously there's very often healing and lifesteal in Arena so, just choose one of them depending on budget atm and ennemy team comp.
Both builds has full CDR (40%) which is essential on Odin and both builds has Relic Dagger so that you can Blink as much as possible. I usually go for Shell has second relic but whatever, you'll just have to choose what you want at that point.
Full Build example 1 (Standard)
Full Build example 1 is a more standard version, with full CDR at 4 completed items in the build and the excellent Genji's Guard and very powerful Shifter's Shield. It is a more damage oriented build, so you still need Reinforced Greaves for additional defense and CC reduction.
Full Build example 2 (Dmg mitigation)
Full Build example 2 is damage mitigation oriented build, which I really enjoy playing and that I feel like it will be the best build out of these two after patch 4.17 release. My favorite in Arena btw. You still build Reinforced Greaves at first back but in late-game, you should sell 'em and build Warrior Tabi for the extra physical power and because Oni Hunter's Garb + Spirit Robe gives 40% CC reduction (which is the cap), so the 20% CC reduction provided by Reinforced Greaves is useless at that point. I would recommand building these first still for the early tankiness but after Spirit Robe's completion, get Warrior Tabi instead. So the idea of this build is that when both Oni and Robe passives get proc, you gain 35% dmg mitigation. A lot of the time this will happens in your ult and so you'll get the opportunity to stay longer and fight longer in your ult without getting shredded and that's a good thing.
Full Build example 3 (Cheap Conquest style)
Full Build example 4 (w/o Relic Dagger)
Full build example 4 is my favorite here and it's very suitable for Clash or Joust and Arena if you don't want to Blink (or get it as second relic). Oni's Hunter Cab passiive works very well on Odin. You shield up, jump on them and ult and get a 20% dmg mitigation for 5s. Plus the 40% CC reduction (from Reinforced Boots and Oni), 40% CCD with Breastplate and Jotunn's and a ****load of MP5 and some pen. Shifter's Shield gives you the power you need when you're under 50% of your total health, so it compensate for building defense boots instead of Warrior Tabi. Just sell Bluestone at the end and build whatever you want ; Masamume for more movement speed and defense, Qinn's or even Exe for boxing potential, Brawler's or Titan for pen. Bulwark might be too much defense but against very high magical damage, like 4 mages it may be a good idea. Remember that Odin gets weaker at late-game so you must be careful but I would usually go for more damage at that point.
Other options / Situational
There's bunch of items that'd be good on Odin but aren't good enough to make it to the Build examples. You might want to experiment and try some of them and may come up with a good build with a different playstyle (and that could be very interesting) but for now on, they better as situational items since most other alternatives are better in my opinion.
On all these builds, even if it's Arena, I do recommend Blue Stone has a start just for the clears, extra mana, damage. It is not a must but that often gave me extra kills and it has proven for me to work and made my playstyle more agressive also. For early-game and even mid-game clears it's kinda essential IMO.
If you come up with some interesting Arena builds with the Other options / Situation items' list, please share in comments. I'll try suggestions and might add other build examples, especially if they require another playstyle and add more depth in the game.
So that's all I gotta say about that. Try these builds and let me know what you think in comments, that'd be appreciated ! I'm proud of Full build example 2 tbh, I think it's a very cool and smart build. Let me know what you think.
VVGL VVGF !