Alright so something to keep in mind that I notice first glance is that the team has a pretty big Ground weakness, between Gallade, Nidoking, M-Haxorus, and Tyranitar. Something that you could use to combat that is Delta Snorlax, which combined with Thick Fat (which eliminates two of its weaknesses) is a solid contender and bulky mon. A common moveset for that is Impish, Adamant, or Careful nature, with Bulk Up, Drain Punch, Seed Bomb, and Earthquake.
Going through the team individually though, I’d remove Thunder Punch for Wild Charge on D. Gallade, since you want something with more power, even if there’s a bit of recoil. I’d also remove both Protect and Power-Up Punch. Other than that, you have a few options. You can use Swords Dance + Ice Shard, Bulk Up + Coverage (such as Leaf Blade, Drain Punch, Knock Off), or all-out offensive with two coverage options plus two STAB moves (Icicle Crash and Wild Charge).
Depending on what nature your Nidoking is, you might want to consider running mixed set, as a mixed set provides more coverage. If there was something you would remove for Delta Snorlax, I’d recommend it to be Nidoking, in all honesty. However, if you don’t want to remove it, you can add Poison Jab or Sludge Wave (depending on nature), and maybe Ice Beam, Thunderbolt, Flamethrower, etc. as coverage options.
Mew seems good. For an item I’d probably go for Leftovers on Mew over Nidoking, and put a Life Orb on Nidoking. Aura Sphere is another option if you don’t want to risk Focus Blast’s accuracy, but Taunt will be useful for one of the Elite Four members (especially if you stick a Lum or Chesto Berry on it as its item).
For Haxorus, I’d remove Dragonify, as you just want to be hitting the opponent hard rather than changing its type. You can either run Dragon Dance + Dragon Claw / Outrage, or Swords Dance + Draco Jet. I’d also add Iron Head for Steel STAB on the Mega, keeping Earthquake is good.
Tyranitar, you don’t need Taunt on two mons. I’d replace it with Stealth Rocks or an Elemental Punch for coverage. Ice Punch could work.
Delta Charizard looks good, nothing I’d change about the moveset. If you know that you’re going to Mega Evolve Haxorus as opposed to Charizard in a battle though, I’d give it either a Choice Scarf or Specs, or maybe Assault Vest / Expert Belt to make it more of an offensive mon and less helpless when there’s another mon that’s Mega Evolved on the field.