Gyarados: I'd get rid of Hydro Pump, as you already have two other Water moves that are pretty good. I'd either replace it with a Physical move and keep the nature, or replace it with yet another Special move and get the Timid nature. The Special move I had in mind was Dragon Pulse. A good move in nearly every situation. It wouldn't be good for Ice, but if you replaced another thing with a Fighting move, you would have some good coverage. Waterfall isn't exactly the best thing in the world, but it's a decent move for getting rid of. The move deleter is in Canalave in case you forget.
Abomasnow: The nature DEFINITELY is not a good thing, mainly for the special defense. Abomasnow is most vulnerable to Fire type moves, which are mostly Special moves. The Attack bonus is good, however. Try to get a Careful nature, as that would lower the Special Attack, which you wouldn't quite need, as the majority of these moves are Physical. Giga Drain has plenty of power, and Abomasnow's attack is pretty good. The moveset is just fine.
Staraptor: Nature is great. The Speed stat is already wonderful and wouldn't be too bad if cut. The moveset, however, is quite awful. The only attacking move in there with more than 5 PP is Fly, which is a pretty shitty move in battles. I would get rid of Fly for some sort of other Physical move of anything that isn't already in there. Another Fighting type move would be just fine though, as it would be pretty good against any Ice types. A Ground type move would also be good for Electric types, but the only Ground type move it can learn is Mud-Slap. The item isn't a very good choice, as its Speed is already very good. I would replace it with Black Belt or Fist Plate, as that would make it as if Close Combat has an STAB bonus. Overall, not too good, but not too bad.
Lucario: Just fine the way he is.
Dialga: I would replace with something ASAP. Maybe some sort of Eevee evolution, or a Drifblim. For Eeveelutions, maybe an Espeon or Jolteon, because Psychic and Electric moves haven't been covered in the team. Drifblim, I'm fairly sure can learn some Psychic moves, so either get an Espeon or Drifblim. Drifblim has some pretty good stats as well, which would be nice. If you got a Drifblim, I would choose Mind Plate. For Espeon, it can learn Ghost moves I am fairly sure, go with the Dread Plate. Jolteon cannot attack Ground types and Ground types would do a good deal of damage to Jolteon, so I'd add a Shuca Berry.
Infernape: Unfortunately, an awful moveset. All the moves have five PP and are either Fire or Fighting. Keep Focus Blast, get rid of Flare Blitz for Fire Punch. Get rid of Focus Punch for Iron Tail, as that would have some good coverage against Rock types. Keep Blast Burn in case you REALLY need some power. Also, get rid of the Wide Lens for Iron Plate, for even more power against Rock types.
Overall, a good team. 7.5/10.