Quick one-over on just the sets...
Xerneas: Seems pretty standard. I'd probably suggest Modest or a defensive nature over Timid since you're running Quiver Dance and, being a Spore + Poison Heal set, will usually get multiple Q.Dances up if you've taken care of your checks and counters first.
Rayquaza: Moves like Earth Power, V-Create, Precipice Blades, and similar are generally preferred over Moongeist on a mixed Aerilate set. Moon is good for Shedinja but... Ray can't switch in on Shedinja anyways and loses if its Focus Sash.
Gengar: Way too fast of a Pokemon to make good use of Core Enforcer. The stuff that naturally outspeeds it are either rare (like Manectric) or typically OHKO (Mewtwo-both). Shell Smash ensures you'll pretty much never remove abilities. Smash also makes Prankster fairly redundant. I'd recommend opting for a Normalize or Mold Breaker Gengar, the latter of which can handle your Shedinja problems.
Chansey: Imposter, so not much to say.
Mewtwo-Y: Mewtwo's unboosted Fakespeed is, I'll be blunt, pretty pathetic, and you're stopped pretty hard by Steel types, especially the uncommon Unaware Steel types. If you wanna do Contrary, V-Create is practically a must. Not entirely, but almost. I'd ditch Fakespeed and pick up some combination of another Contrary move (V-Create or special attack move like Overheat), a coverage move, and/or a utility move like Taunt or, since you have Goggles, Spore.
Mewtwo-X: This set is... uhhh... I can't really think of anything good here, to be fully honest. Mixed Skill Link with no STAB just seems... bad. This set just needs to be scrapped entirely and either made into a different Xtwo set, a different Skill Link set, or a different Pokemon altogether. If you opt for Skill Link though, Kyu-B is probably your most viable option with a set along these lines....
Kyurem Black @ Life Orb / Lum Berry / King's Rock
Ability: Skill Link
EVs: 240 HP / 252 Atk / 252 Def / 252 SpD / 252 Spe
Adamant Nature
- Icicle Spear
- Bone Rush
- Bullet Seed / Sunsteel Strike / U-turn
- Shift Gear / Shell Smash / King's Shield
Overall, there's some major problems on your team. Here's what I can tell without doing an offensive or defensive type coverage analysis or playing it myself...
-Imposter-weak. Other than Xerneas, Imposter can come in and wreck your team with relative reliability. Gengar can be Spored and then bopped with Core Enforcer to prevent it from priority sleeping opposing Chansey. Your Fakespeed doesn't do enough damage to stop Imposters of move of your sets. If Imposter beats your Mewtwo-Y after it's obtain some boosts, it's pretty much good game for you.
-Shedinja-weak. Your only option is Moongeist on Mewtwo X and Rayquaza, neither of which can switch into Shedinja and lose 1 v 1 to Focus Sash variants. Recycle Focus Sash can defeat your whole team if played well. Gengar can't beat Sturdy Shedinja, just annoy it unless Shedinja is running Spectral Thief, in which case Shedinja wins eventually. Endeavorless sets don't threaten you directly, but they wall you near endlessly.
-Hazard-weak. You have no way to set hazards or remove them and your only option to stop them from getting up is offensive presence. If a balanced or stall team manages to set Rocks against you and then stop your momentum, they can pretty much just wear you down with hazards with proper play.
-Anti-Imposter weak. If something like Dazzling Gengar gets going on you, you lose. There's several other anti-Imposter sets and cores which can set-up and then sweep the rest of your team too if they get the opportunity. Ray's Fakespeed helps with this, but doesn't answer bulky set-up very well, such as Shift Gear Posion Heal Regigas.
-Team synergy. Nobody really seems to cover anyone much, offensively or defensively. Xerneas dealing with other Dragons for Ray and Dark-types for half your team is the best point. But nothing covers Xerneas' Steel-weakness other than Xern's Earth Power, which most Steels can tank if Xern isn't set-up well while Celesteela doesn't give a crap and Ferrothorn doesn't care too much. Granted, I don't do offense heavy teams super well, since I know you can get pretty far ignoring synergy and overwhelming your opponent with six Mewtwos or something, but I find a team that's able to check and counter each other's threats works much better.
Example of synergy: Yveltal and Solgaleo make good partners both offensively and defensively. Yveltal cover's Solgaleo's weaknesses to Dark, Ghost, and Ground and can force out or defeat Ghost-types trying to take advantage of Solgaleo. Solgaleo, meanwhile, can take Ice, Rock, and Fairy attacks for Yveltal and can defeat all three types with its Steel-type moves. It's not a perfect duo, however, since Solgaleo's Fire weakness and Yveltal's Electric weakness are uncovered, but it's certainly one of the stronger pairings out there and both of them can be covered easily by a third partner, such as Giratina, Zygarde, or Primal Groudon.