Pokemon: Dialga
New Ability: Time Dilation
Description: While this Pokemon is on the field, all end-of-turn effects occur twice, and all field effect expend 2 turns per turn.
Reasoning: Basically time moves at double speed, giving double Leftovers returns, double Toxic damage, double Leech Seed, etc. Weather, Trick Room, Reflect and every other move that has a set turn duration will burn twice the amount of turns each turn. This gives Dialga a sneaky niche on stall that amps up passive damage while increasing healing, all while screwing over teams that rely on field effects. Of course, this goes both ways, though thankfully Dialga cannot be poisoned.
Pokemon: Palkia
New Ability: Wormhole
Description: While this Pokemon is on the field, all healing and stat-boosting effects are instead gained by the adjacent Pokemon,
Reasoning: You rip portals in space to swap moves, functioning on the same principle as Snatch, using the same list of affected moves. Like Dialga, this ability goes both ways, but Palkia is rarely known to use anything but attacking moves, so you can switch into a predicted heal or boost to grab it for yourself. You can even play mindgames with Xerneas, as you can steal Geomancy, but also die to a Moonblast prediction.
Pokemon: Giratina
New Ability: Banishment
Description: While this Pokemon is on the field, all Pokemon with 6 or more stat boosts faint instantly.
Reasoning: Giratina was banished for its violence, and is shown to have some affinity for death and afterlife, so I gave it the ability to smite the fools that reach beyond their power. Also serves well for the Giritina-as-Lucifer motif, and links in the "6" theme (6 wing spikes, neck spikes and legs -- 666). Competitively, you laugh at Geo-Xern, put a timer on a Blaziken sweep, and halt Calm Mind users from getting too greedy. Supports your role as a wall by giving you a way to deal with setup sweepers other than phazing. Just don't set up 3 Calm Minds yourself...unless you want to die.
And just in case Giratina-O gets its own...
Pokemon: Giratina (Origin)
New Ability: Flipside
Description: While this Pokemon is on the field, all stat changes are reversed.
Reasoning: Draws on the Distortion World side of Giratina (as it is in Origin form), forcing Contrary on the entire field. Also, forms a counterpart to Giratina-A's ability. Stat boosters will fail, Blaziken gets slower each turn, and Draco Meteor gives you +2. Note that as you cannot hold a Scarf and aren't that fast, you can be revenge killed by a Draco Meteor that will also give your enemy +2, and you yourself cannot use a Calm Mind set.