First I have a level 100 Aricuno-it knows Hail, Blizzard, Ice Beam and Fly
Blizzard with Ice Beam is redundant.
A decent Articuno move set would be: Substitute, Roost, Protect, Ice Beam/ Whirlwind and Leftovers as an item.
If you can get a Sub up Articuno will stay alive for a good 20 turns, if your opponent attacks they will lose 2 PP every turn (40 max), if they switch they'll be damaged from any entry hazards you've put up.
Next is a level 100 Moltres- it knows Solar Beam, Aerial Ace, Flamethrower, and Steel Wing
Steel Wing is useless here and Air Slash is better than Aerial Ace.
Try using U-Turn to deal some damage and switch.
Then comes my level 100 Zapdos- it knows Rain Dance, Thunder, Roost, and Drill Peck
Use Thunderbolt over Thunder and Heat Wave over Rain Dance.
I have a level 100 Lugia- it knows Aeroblast, Hydro Pump, Extrasensory, and Sky Attack
Sky attack is powerful, but your opponent will just switch to a counter on the next turn.
I prefer to use Surf over Hydro Pump.
Lugia is the best Pokemon to use Roost.
After that is a level 100 Ho-Oh- it knows Fire Blast, Sacred Fire, Extrasensory, and Ancient Power
Take off Fire Blast and use Earthquake for Heatran.
Ancient Power is fairly useless unless it raises your stats which won't happen often and when it does most decent players will Phase it.
Then last I have a level 100 Groudon- it knows Fire Blast, Slash, Fissure, and Solar Beam.
Try Earthquake, Swords Dance, Stealth Rock and Stone Edge.
Over all you have a major weakness to Rock and Electric.
Half of your team (Moltres, Articuno and Ho-oh) will lose half of their health when they switch in to Stealth Rock and the only Pokemon that will lose less than a quarter is Groudon (you really need a Pokemon that can learn Rapid Spin).
Electric + Ice is a common combination on most teams, so you can't be completely reliant on Groudon to take Electric attacks.
All of the Pokemon you have that aren't weak to Ice will lose half of their health to Stealth Rock so Ice attacks are another big problem especially if your opponent has put SR down.