Also, I saw someone using a Mega Abomasnow once on a Trick Room team. Would it be better to run mixed (with Wood Hammer for Kyogre) or fully special?
Anyway, for Obamasnow:
4 Atk Mega Abomasnow Wood Hammer vs. 252 HP / 0 Def Primal Kyogre: 188-224 (90.8 - 108.2%) -- 43.8% chance to OHKO
I'm not sure what Pogre typically runs for HP/Def balance but you can probably OHKO it with a reasonable amount of investment. Grass Knot can solidly 2HKO it, if you'd prefer a no-recoil, pure Special alternative.
Keep in mind that if you run Wood Hammer, you take recoil but more importantly you lose the KO if you get Intimidated. Luckily, most people aren't stupid enough to park Landog / Mence in front of Obamasnow, but you never know.
Grass Knot also takes a chunk out of Pdon:
252+ SpA Mega Abomasnow Grass Knot (120 BP) vs. 252 HP / 0 SpD Primal Groudon: 124-147 (59.9 - 71%) -- guaranteed 2HKO
Pdon will obviously murder you with Fire STAB, but if you have TR or Heavy Rain up you can take it on with the right partner. Abomasnow learns Role Play, so you could run something like Ogre + Obama in TR.
edit: never before have I said this, but Abomasnow might actually be good here.