Well, I'm not sure what movests to have with these particular pokemon I have now, so feel free to put in a comment! (I'm also not puttin in lvls because I'm training all of them to lvl 100 the old-fashioned way.)
Luxray
Current Movset:
Ice Fang
Spark
Crunch
Return/Fire Fang
If you're unable to get Ice Fang, you could consider Iron Tail instead. Luxray is more of a physical Pokemon, so you don't need Thunder. It's also generally not a good idea to have two of the same types of damaging moves on one Pokemon. In this case, you had Thunder Fang and Thunder. Her Attack is superior to her Sp.Attack, so drop Thunder. Also, Thunder is inaccurate. Spark might not make the opponent flinch, but it does have a better chance at paralysis iirc and is more accurate than Thunder Fang. Return with max happiness is MUCH more powerful than Strength. Actually, a Return from a happy Luxray is her most powerful attack when against neutral opponents.
Dragonite
Current Moveset:
-Dragon Dance
-Outrage (Or keep Dragon Rush)/Dragon Claw
-Thunder Punch/Fire Punch/Thunderbolt/Flamethrower
-EQ
EQ plus a Fire/Electric is going to cover more than Water attacks are. Besides, you don't need Surf AND Waterfall on the same set. Both are effective/not effective against the same types of Pokemon. I'm not a big fan of Dragon Rush's accuracy, so Dragon Claw is a solid way to go. Hyper Beam leaves your Dragonite COMPLETELY open to a revenge kill if you're planning on using her competitively (as you stated). Drop Hyper Beam for Dragon Dance. With DD, you're able to boost her decent Speed to sweeping levels, and boost her already very high Attack. DD + STABed Outrage = hurt
Staraptor
Current Moveset:
Brave Bird
Quick Attack
Close Combat
U-Turn
She's gotta have Close Combat! :O lol Fly takes too long to use, and you already have the superior Brave Bird. If you're not a huge fan of recoil, you could consider Aerial Ace over Brave Bird. Other than that, this looks good.
Flareon
Current Moveset:
Fire Fang
Quick Attack
Iron Tail/Toxic
Return/Will-O-Wisp
This is one of those cases where it's okay to have two of the same types of damaging moves. Flareon's movepool is so shallow, it doesn't even come past your toes. Anyways, the deal is get STAB for Fire Fang, her only physical Fire attack, and hope for some big damage. She has a HUGE Attack stat, so that shouldn't be too hard to achieve. Quick Attack is nice for faster, fragile opponents that need to be finished off. The rest of the set is up to you: pure offense or double status. She has the Attack to hold the Choice Band, but you could consider WoW for physical opponents, or Toxic against Water types and others.
Garchomp
Current Moveset:
Earthquake
Dragon Claw
Stone Edge/Fire Fang
Swords Dance
After a Swords Dance, she WILL hit hard. She's more of a physical Pokemon, so don't teach her Dragon Pulse. Take Down isn't super-effective against anything, gives recoil, and Garchomp has much better physical options, so drop it. Also, Sand Storm might help out your Garchomp, but what about the rest of your team? All of your other Pokemon are going to take damage from Sand Storm if you switch out Garchomp/if Garchomp faints. "Will it help my team or just one member?" It's important to remember that when picking weather moves.
Spiritomb
Current Moveset:
Nasty Plot/Calm Mind
Hypnosis/Will-O-Wisp
HP Fighting/Psychic
Dark Pulse or Shadow Ball
Dark and Ghost attacks are SO similar. It's generally not a good idea to
not have both offensive Ghost and Dark attacks on one MS. In the last slot, Shadow Ball really would be a superior choice due to the chance of Shadow Ball lowering the opponent's Sp.Defense, which could help your setting up. Spiritomb is so slow that it won't matter if the opponent flinches because you'll be going after the opponent 99% of the time with Spiritomb. lol
I'm also using this as an online team. Whaddya think?