Alright, now that I'm on a computer, I will put a few more sets.
SpecsQuayza
Nature: Modest/Timid
EVs: 252 sp attack and speed, 4 HP
@: Choice Specs
Draco Meteor
Fire Blast/Overheat
Earth Power/Extremespeed
Dragon Pulse
A pretty basic Specs set. Earth Power is for Heatran while still hitting Dialga, Reshiram, Zekrom, Excadrill, and others. You could opt for Surf or Focus Blast instead. It may seem odd to pair Draco Meteor with Overheat, but the fact that you're locked by Choice Specs means you will be switching anyway.
How do you Dance without legs?
Nature: Adamant/Jolly/Lonely
EVs: 252 attack and speed, 4 HP/sp attack if you opt for Fire Blast
@: Life Orb
Dragon Dance/Swords Dance
Outrage
V-Create/Fire Blast
Extremespeed/Earthquake
A stat-boosting setup. Rayquayza has trouble pulling off stat boosts because of its issues switching in, but if you pull off one boost, things get fun fast. Dragon Dancers should not use V-Create as the speed boosts will be erased.
MixQuayza Dancing
Nature: Mild
EVs: 248 attack, 252 sp attack, 8 speed
@: Life Orb
Dragon Dance
Outrage
Overheat/Fire Blast
Earthquake/Earth Power/Extremespeed
Pretty straightforward, but that's what Rayquayza does best. Dragon Dance for boosts. Outrage is the STAB move to use because it is powerful (unlike Dragon Claw and Dragon Pulse) and does not drop your stats (like Draco Meteor). Overheat gets mentioned here again, but if Overheat is not Quayza's only special attack, use Fire Blast instead. V-Create should not be used because of the speed drops. The last slot depends on whether you need priority or a way to take down Heatran.
Other options:
Air Slash is another STAB move, but Outrage and Draco Meteor make Air Slash useless.
Quayza has access to a large number of extra coverage moves in Thunderbolt, Thunder, Surf, Ice Beam, Energy Ball, and Focus Blast on the special side, as well as Stone Edge, Waterfall, Crunch, Brick Break, and Aqua Tail on the physical side. However, with Focus Blast being the possible exception, all of these moves will deal less damage than Quayza's Outrage and Draco Meteor, as well as Fire Blast and Overheat.
I will give Thunder a second mention as a way to put Kyogre down. However, even with Kyogre around, Thunder will have 70 accuracy because of Rayquayza. You should do fine with Outrage or Draco Meteor anyway.
Flamethrower is the weaker and accurate Fire Blast. In the Uber tier, Flamethrower does very little, making Fire Blast and Overheat much better choices.
I have now completed my Quayza for POTW. Enjoy!