Ahh, so this is why Etesian got his hand tight. Let me throw my 2 cents out of my pocket. Decided to look up your team move pool and this is what I got. The problem isn't the team but rather the moves it got. Although, I'm not Etesian so I keep everything short
Delphox: Interesting Type, never seeing Fire and Psychic. Give it Heat Wave, I wish I could had it for my Ninetales. Will-O-Wisp or Light Screen, I like Will-O-Wisp more. Psyshock for STAB and Shadoll Ball for coverage.
Clawitzer: I'm scratching my head thinking "what are you doing?". This thing is awesome: Aura Sphere, Dark Pulse, Dragon Pulse. Water Pulse and with %50 boost power??? that's basically STAB. Tons of coverage too...the only flaw I see about this guy is it speed which can be fix with support. You can choose between Water Pulse and Surf but I would personally prefer Water Pulse (chances of confusing the enemy), Surf is only good for double battles.
Braviary: Take out Slash for Superpower and Sky Drop for Tailwind. Tailwind helps Clawitzer/Tyrantrum/Scrafty sweep for days
Scrafty: Breed with Dragon Dance, with its defense it should be able to set up with not much trouble plus it helps itself on speed. I agreed with Etesian, breed it with Rock Slide or Stone Edge; Head Smash is not so good with Scrafty due to his poor HP. HJK is good and Crunch has well (although you do have lots of Dark Moves so you can switch that Crunch for Zen Headbutt covers Poison and Fighting)
Tyrantrum: Switch his ability to Rock Head so he doesn't take damage recoil damage with Head Smash (you can spam Head Smash for days). Change Crunch for Dragon Dance, it will be able to sweep.
Since you plan to change Luxray for something else I recommended a Steel Type. You have nothing on your team that can defeat Fairy Types