Zappa's air game is some pretty weak shit, but he has a few tools/tricks he can use.
For naked/sword, you can space a jump in j.k>j.s and it'll be safe, then do whatever ground string from there. Always try to end a sword string in swipe for the knockdown, then shenanigans away. Sword also has j.p>j.h, but only recommended after a knockdown.
Naked has j.h, which takes some time to get used to but is pretty nice once you get the hang of it. If you land close to them, you can go into c.s, otherwise just 5p/2k/whatever.
Ghost has j.h, the greatest crossup gimmick in the game. Gives knockdown. Run at them, jump over j.h. Do the same, but airdash backwards immediately j.h. Jump over slow j.h. Best shit ever.
With dog I try to use 8D with jump over/airdash backwards jukes. Decent way to get orbs, but you lose pressure. On the bright side, it pisses your opponent off.
With Raoh you can do a rising j.s>j.p, then jc to make it safe. Jumping in, j.s has great horizontal reach, and I'm pretty sure it goes into j.d.
Zappa's weird, but he's fun to play when you get used to what he has and doesn't have. For the most part, stay grounded so that your air tricks are unexpected and land when you pull them out of the bag.