I'm going to assume that you aren't able to/don't want to switch any of the Pokemon.
Azumarill really needs to have Huge Power as its ability to be used. Brick Break/Focus Punch should be used then for some type coverage. Also Rollout is a bad choice as it means you can't switch and you will probably miss/faint before it becomes good. Double-Edge is a good move to have and Ice Beam could be used to beat Drake.
Nosepass needs to get rid of Rock Smash. Keep Rock Slide as it is good STAB and keep Thunder Wave as Nosepass can't really deal much damage to begin with so it will be helpful to induce some status. Other moves you could consider are Earthquake, Thunderbolt and Toxic.
Minum should keep Thunder Wave and should be taught Thunderbolt. You could also consider teaching it Iron Tail for some more type coverage.
You could consider have Grumpig use Calm Mind to boost its stats. Psychic is a must. You should probably keep Confuse Ray as it could be useful. It has a really bad special movepool, so you may have to use Shock Wave and if possible, a good special typed Hidden Power.
I assume Fly is a must for Skarmory for transportation. Aerial Ace is the best STAB move available, along with Steel Wing. Toxic and Spikes are good moves to consider also.
Soon to become Delcatty should have its not bad movepool abused. Thunderbolt, Ice Beam, could be used for coverage, but they will do weak damage. Return/Double-Edge is a must for bigger damage. Shadow Ball is good for coverage. Assist might seem tempting, but you'd have to be really lucky to use it. Sing is a good and risky move to induce sleep.
Overall, if possible, I suggest a huge change in your team. Skarmory is the only worthwhile one I can see in your team. The rest have really weak base stats or movepools or both.
I prefer Aerial Ace over it, since it's a guaranteed hit and more power, along with priority.
Aerial Ace doesn't have any extra priority.
If you do pick new Pokemon, remember to consider all the big opponents you will face, and their Pokemon and their moves, and work with that.