Umbreon is a bizarre Pokemon. He can fill quite a few roles effectively, but has to compete with so many outright better Pokemon for the job that he is left with basically nothing to himself. As a special tank, he must contend with the behemoth that is Blissey, and as a Curse sweeper, he will always live in the shadow of Tyranitar. As a result of this, Umbreon's usage truly is bottom of the barrel in OU.
It's not all bad for Umbreon, however. Umbreon's value for Baton Pass teams is unquestioned with his ability to pass the coveted Mean Look. Outside of that, Umbreon likes long walks on the beach under moonlight, a good horror flick, and popcorn. If that weren't enough to convince you to use him, he also happens to be one of the most adorable Pokemon in the tier. More realistically, if you're not using Umbreon to Baton Pass Mean Look, don't use Umbreon.
Fortunately for Umbreon, he happens to be the best at one thing and one thing alone: Baton Passing Mean Look. Mean Look's value may not be obvious at first glance, but with further investigation, it can sometimes mean the difference between winning a game with a Baton Pass team or losing it. Mean Look prevents the opponent from switching out, potentially allowing your Baton Pass chain to complete unopposed if you play your cards right.
Baton Pass and Mean Look form the basis of this set, allowing Umbreon to lock in an opponent and then pass off to something that can set up on whatever is trapped. Wish is a very good move to have in a Baton Pass chain, healing whatever you Baton Pass to or keeping Umbreon healthy as he tries to accomplish his job. In the last slot, Taunt is the preferred move. It is of utmost importance that Umbreon get off a Taunt first so as to not get Taunted when attempting to setup. Yawn can be incredibly valuable for forcing a second switch after your opponent's primary switch-in to Umbreon rears its ugly head. If this plays out right, Umbreon will be able to use Mean Look as the opponent brings out a mediocre Umbreon check at best. Protect is still an option to guarantee that Umbreon's Wish heals him, though, and can be useful in certain circumstances.Team Options & Additional Comments >>>
Umbreon's movepool is about as barren as most Eevee evolutions. He has access to attacking moves in the form of Payback, Pursuit, and Dark Pulse to do some damage, but with those attacking stats, "some" damage is an overstatement. On the support side, Umbreon has Moonlight, Fake Tears, Screech, and Confuse Ray. Moonlight is almost always worse than Wish in a sandstorm-infested metagame, while the rest of the aforementioned options are underwhelming at best.
Umbreon can run a set of Curse, Payback, Wish, and Protect to attempt a sweep. Tyranitar runs this set better on almost all counts, though, with much higher Special Defense after the sandstorm boost, better HP, the ability to take status, and an almost absurdly higher Attack stat. The only reason you might use Umbreon over Tyranitar is that he doesn't have Tyranitar's Water-, Grass-, Ground-, Steel-, and extra Fighting-type weaknesses. Umbreon can also attempt to run a Wish support set for his team, but Blissey uses the same set infinitely better with her obscene special bulk. Umbreon can also make use of Baton Pass in one more way by passing Curse boosts to sweepers, but it is largely ineffective, and those turns are better spent having other Pokemon pass Swords Dance or Agility boosts.
Checks and Counters
Just about anything with a high-power Fighting- or Bug-type attack will send Umbreon reeling. Scizor is an especially terrifying check to Umbreon because he can maim Umbreon with U-turn and scout your team if you switch Umbreon out. Heracross, Machamp, Lucario, and Infernape all give Umbreon a lot of problems by resisting Dark-type attacks and threatening to OHKO in return. Despite the fact that Umbreon is not physically frail, the majority of super-powered physical attackers in OU, such as Metagross and Tyranitar, will shred Umbreon to pieces with neutral STAB attacks. Taunt users in Aerodactyl, Gyarados, and Azelf will give Umbreon issues if he is without an attack. Gyarados also threatens to set up on Umbreon, making him that much more deadly.