I'm going to break my analysis into two parts
ARIA FORM
I'm really not impressed. Latios is much better. Abusing Serene Grace is pretty tricky since there isn't much to abuse it with.
Boosting Sweeper
Nature: Timid
EVs: 252 sp attack and speed, 4 hp
@: Life Orb
Charge Beam/Calm Mind
Psychic/Psyshock
Shadow Ball/Hyper Voice
Focus Blast/Hyper Voice
Charge Beam lets you boost without being crippled by Taunt, but ground-types can stop that, so Calm Mind can be used instead. Psychic hits harder, but Psyshock deals physical damage. Shadow Ball and Focus Blast add coverage while Hyper Voice is extra STAB.
Choice
Nature: Timid
EVs: same as last
@: Choice Specs/Choice Scarf
Psyshock/Psychic
Shadow Ball
Focus Blast
Hyper Voice/Relic Song/U-Turn
Choice attacker is a choice attacker. Relic Song will power down every other turn. Also, if you sleep something with it, you will be forced to switch due to sleep clause. U-Turn scouts.
Basically, just use Latios. It's way better.
PIROUETTE FORM
Now THIS is scary. You are restricted to three moves because the fourth slot requires Relic Song. Also, You can't run a choice set because of it. However, something that hits about as hard as Terrakion and is super fast? Terrifying!
Meloetta does Haruhi Suzumiya's Hare Hare Yukai!
http://www.youtube.com/watch?v=_indP8fT494
Nature: Adamant (this thing is plenty fast)
EVs: 252 attack and speed, 4 hp
@: Life Orb/Muscle Band/Leftovers
Relic Song
Drain Punch/Close Combat
Shadow Claw
Stone Edge
The main issue is that Meloetta has three-moveslot syndrome for this form. There is no room for dual STAB or a boosting move, so everything comes down to Meloetta's raw stats. Thankfully, those are quite huge. Relic Song lets Meloetta change form, so it's required. Drain Punch is awesome with Life Orb, but Close Combat will pulverize everything that doesn't resist or is immune. Whatever else is handled by either Shadow Claw or Stone Edge.
Meloetta sings and dances Lucky Star's Motteke! Sailor Fuku!
http://www.youtube.com/watch?v=nAOB0Xx9o3I&feature=related
Nature: Hasty
EVs: 252 speed, 120 attack, rest special attack
@: Leftovers/Life Orb
Work Up/Shadow Ball
Relic Song
Close Combat
Psychic/Shadow Ball
The fact that Meloetta changes form in battle can be a major hassle, but it can also work in your benefit. Relic Song lets you swap to the stat that you need while possibly shutting down an enemy. Work Up is the boosting move. Close Combat is Physical STAB while Psychic is Special STAB. Work Up or Psychic can be dropped for Shadow Ball if type coverage worries you.
Other options:
While slower, Terrakion has superior type coverage behind STABs.
Fire Punch hits Skarmory and Bronzong and Scizor, but has little use otherwise.
Countering:
Paralysis is your friend. Neither form likes paralysis. Otherwise, a good Mach Punch from Conkeldurr will do the job after entry hazard damage is factored in. Sableye and Spiritomb wall Meloetta 100% if Meloetta does not have Shadow Ball or Shadow Claw, which is more common on mixed attackers. Physical Meloetta is handled by simply switching in any Ghost type because Relic Song will fail and shut down Meloetta completely. Physical Meloetta also has the problem of being forced to rely only on her raw stats because Relic Song takes up a move slot, leaving her with only three usable moves. Also, locking Meloetta into Relic Song with Trick+Choice Item or Encore. One last thing you can do is phaze this thing. Physical Meloetta hates being phazed.
I didn't mention much about Special Meloetta. The reason is because Special Meloetta really isn't much of anything special. It's just Gardevoir on steroids and a normal typing. Chansey or Blissey can handle Special Meloetta as long as Meloetta does not have Psyshock.
The main thing to remember is that Meloetta is something that can swing momentum in your favor, but will have trouble maintaining it.