Sunny Day on that Delphox of yours won't really do much. It boosts Delphox's STAB, but harms Swampert's. Also, 2 Psychic attacks may not be that good, I say you keep just Psychic. Personally, I also hate Fire Blast's accuracy, so Flamethrower could be better, it's barely weaker, or perhaps Heat Wave (Torkoal/Growlithe). HW has more power than F.thrower and also hits both foes in double-battles.
For new moves, Flame Charge for Speed, Trick Room for "Speed", Will-o-Wisp to cripple and defend and Light Screen to defend are all worth considering.
Bite and Shadow Ball have the same S.Effective coverage, while Noivern is a Special Attacker, so ditch Bite. And maybe get Air Slash instead of Hurricane, for the same reasons as above and also because a 30% flinch chance is very useful.
Instead, Tailwind for overall Speed, Boomburst for power, Super Fang for wall-breaking or as a good "parting shot" of sorts, or Flamethrower (although Steel is the only type gym weak to Fire which we have yet to beat, it could still be quite useful).
I don't know what Ability you've got on this guy, but there's a Toxic Orb in the game since E13. Give this guy Guts and he'll hit way harder. Also, ditch Strength for either Fake Out or Bullet Punch.
Defense boosts are also wasted on Hariyama, since it suffers from, as I dub it, "Wailord syndrome" : ridiculously high base HP, no defense stats. Brave or Adamant would be much better for this guy.
Bite and Shadow Ball again, keep only S.Ball again. I'll assume Rain Dance was entirely for Charlotte.
You should definitely go for Grass Knot, as all gyms Grass is super-effective against are still coming up. If you're against a foe against you know you won't do much damage, but can (most likely) outspeed, then Yawn is a great move for Espeon. And then there's also Hidden Power, Fighting would be great/best/ideal.
I'll agree with the above, Moonblast over Fairy Wind. Wish'll do as the third move, and for the fourth move (having Lucky Chant is pointless), Hidden Power or, if you don't want to be locked into Petal Dance, Grass Knot.
Ditch Surf and Rock Smash. There's plenty of way better moves for Swampert, such as Avalanche, Hammer Arm/Brick Break, Endeavor, Curse and Double-Edge,, maybe Yawn.
For natures, I'd recommend Modest or Timid for Delphox, Noivern and Espeon,
Adamant or Brave for Hariyama,
Adamant/Impish/Careful/Brave/Relaxed for Swampert,
Modest or Calm for Flogres (it's got no physical defense, might as well put it all into it's Special Defense then, eh?)
For abilites, since you didn't state them, I'd say go for, in order, Magician, Frisk, Guts, Magic Bounce, Whatever and Torrent (or Damp, doesn't even matter that much).