Azelf is one of my favorite leads due to it being quick and having high base Attack and Special Attack. It also learns Taunt and Stealth Rock, which are 2 very useful moves.
Shaymin is a little cute rodent that can deal some heavy damage. Seed Flare usually dents anything that it hits, aside from Pokemon that resist it. Shaymin is also the Grass type of this team, which is important due to the Grass / Water / Fire core that I am using.
Empoleon is the wall of this team. He acts as a check to the Ice types that can threaten this team as he resists Ice. He is also the Water type of this team.
I wanted something that can hit hard, and Victini was a perfect choice in my opinion. Choice Banded V-Create will pretty much demolish anything in it's way, as 180 base power is frightening, and near 500 attack backing it up just makes it terrifying. Victini is the Fire Type of this team which completes the Grass / Water / Fire Core.
Flygon is the scarfer on this team, as pretty much all UU teams have a Scarfer. It also provides needed STAB moves that kill some threats that can threaten my team.
Raikou is the last Pokemon on this team, and it's second special attacker. It can set up on some Pokemon that will come in and try to wall some of my physical attackers like a Suicune, and can proceed to sweep.
In-Depth Analysis
Blue (Azelf) @ Focus Sash Trait: Levitate EVs: 4 HP / 252 Atk / 252 Spd Adamant Nature (+Atk, -SAtk) - Stealth Rock - Taunt - Zen Headbutt - Explosion
Azelf is the lead of this team. It sets up Rocks, and can also prevent the other team from setting their hazards up. Zen Headbutt can deal some damage to Pokemon and Explosion is just downright powerful.
Green (Shaymin) @ Life Orb Trait: Natural Cure EVs: 4 HP / 252 SAtk / 252 Spd Modest Nature (+SAtk, -Atk) - Seed Flare - Hidden Power [Fire] - Earth Power - Rest
Shaymin is a pretty good special attacker. Seed Flare is it's main move, as it deals nice damage and had a very nice Special Defense drop percentage. Hidden Power Fire is for other Grass types trying to wall this little rodent and Earth Power is for Fire types like Houndoom and Arcanine. Rest is for it can restore all it's health back in one turn.
Empoleon is a very good wall with a nice typing. Scald is it's main STAB move and has a nifty 30% burn chance. Ice Beam is for Dragon Types such as Flygon, who is a nuisance to this team. Knock Off is for Pokemon who rely on their item, like a Choice Scarf Darmanitan or a Choice Band Azumarill.
Red (Victini) @ Choice Band Trait: Victory Star EVs: 4 HP / 252 Atk / 252 Spd Adamant Nature (+Atk, -SAtk) - V-create - U-turn - Fusion Bolt - Zen Headbutt
Victini is the physical powerhouse of this team. V-Create just murders everything. U-Turn is to scout and also works nice with the other Pokemon on this team. Fusion Bolt is for Water types trying to attempt to sponge V-Create, but get hit by a Fusion Bolt instead. Zen Headbutt is a STAB move that helps it kill off some Fighting types with no need to sacrifice it's defenses and speed.
Green #2 (Flygon) (M) @ Choice Scarf Trait: Levitate EVs: 4 HP / 252 Atk / 252 Spd Adamant Nature (+Atk, -SAtk) - Earthquake - U-turn - Outrage - Stone Edge
Flygon is my scarfer and it has some synergy with the rest of the team. Ground / Dragon are pretty awesome STABs to have, as they have very powerful moves and have good coverage. U-Turn is to get out of some situations and Stone Edge is for some Flying types.
Yellow (Raikou) @ Leftovers Trait: Pressure EVs: 128 HP / 76 Def / 52 SAtk / 252 Spd Timid Nature (+Spd, -Atk) - Substitute - Calm Mind - Thunderbolt - Hidden Power [Ice]
Raikou has synergy with Victini, as it provides a check to many water types. Substitute is for Raikou can hide behind a substitute while attempting to set up. After it has set up, it's pretty much GG unless you have a Powerful Scarfer. Thunderbolt and HP Ice are it's attacking moves and have good coverage.
Maybe U-Turn over Stealth Rock on Azelf. With this, you can put Claydol with SR and Rapid Spin. You can try Azumarill over Empoleon to have a new physical attacker.
I love Manectric + Azumarill, but Raikou is the best eletric type on UU.
Actually, Drought Vulpix is banned in Smogon UU, so it's not available there Vast.
Anyway, the only thing I would really consider is Zapdos over Raikou in order to solidify a defensive core with Empoleon. Other stuff I would suggest is mainly nitpicky stuff, but just look into Timid nature on Shaymin, Fire Blast on Flygon, and U-Turn on Azelf.
Eon80, I had thought of Zapdos, so I probably will change Raikou to Zapdos. Hm, I didn't really think of Timid, seeing as Shaymin's speed is acceptable for me. I just used the Azelf that I use in OU, so I will change that.