On Expert? How? :v
My fafnir has lv10 elemental attack up and a rank 7 stone on top of that, rank 10 fire sword with a rank 9 stone on top of that, and he can do about 300x10 damage with fire wave. I have Ariana's Attack Order at 10 with a rank 9 stone on top. He can do that on turns 2 and 3 (if not paralyzed on turn 2 by judgement), then spends a turn to extend, or use meteor smash since its damage/tp is so good). By then he's usually paralyzed or feared or cursed and either kills himself or loses a turn or two. Fafnir's damage is good but he's not that good...
Flavio and Chloe are basically useless to me on this fight until Flavio can land Blind Arrow (takes 4 turns sometimes) so that Chloe can do high damage with Ailing Slash, and Ariana can only do so much with Corrupt Howl wiping all my buffs and slamming me with curse or fear by turn 5. I usually spend turn 1 throwing Air Slash to give me better odds of landing a Blind Arrow (which, even with lv17 Curb Atk Up, lv7 curse mastery, lv 8 Triple Charge, and lv10 Blind Arrow, still usually won't stick, even after Air Slash).
If I wasn't getting hit by 3 ailments and 3 binds I could probably win this easily but I don't know how I could ever kill him fast enough with this party to not have to worry about them.
Of course on expert. Storm Emperor only has 32000hp on expert, so you should kill him easily if you stack your buffs well.
Alright,
I refreshed myself a bit on the fight. Gamefaqs has a super helpful community when it comes to boss strategies, so most of my advice actually comes from what I've learned from there.
So, the first trick is to leg bind him on turn 1 and head bind on turn 2. That stops judgement on turn 2, since the first 3 moves are constant and makes him weaker to elemental damage. For this, you'll want to set up the first 2 turns like i did, focus on getting leg bind the first turn, then head bind after. Since I had a hexer and dark hunter, getting leg/head bind were simple but it may be harder for you depending on how you built you WM and S.
If you can lock Stormy down in the first 2 turns with leg and head bind, he'll be extremely limited in his options, and won't be able to use Corrupt Howl. During that time you need to focus on set up, which is the second trick and what makes quick kills work. This is really up to you how to get it done, but you'll be looking for a burst damage set up. Use Fafnir and Princess to buff your 3 attackers, Protector will focus on limiting damage (Volt guard turn 1, if the leg bind lands then 2 turn he can help buff, turn 3 is front guard for the incoming basic attack). Survivalist and War magus should be able to land the binds between the two of them (Force boost WM if need be). You'll want to use a prelude on each along with attack order and if possible Flame Fantasia (or some other elemental debuff on the dragon). This should set you up for major damage for a few turns, so force boost, use a high level circle and go. Prelude + circle + attack order + enemy head bind + elemental debuff all fully stack with each other, so not much will live through it.
You should be safe until turn 4 with the strategy, so just make sure to unload on turns 3 and 4 and he should fall over. If it looks dangerous and you are close, remember to focus on damage, and use your protector's force boost to buy the turn. If it still looks iffy you may have to gamble, but in that case your damage set up may need some work.
As a side note, most buffs/debuffs don't stack fully, but have diminishing returns so they aren't useful together. Preludes multiply all damage as a separate calculation, similar to how circles work so they can be stacked with a regular buffs and circles. The idea buff situation is prelude + normal buff + circle on your side, and head bind + physical/elemental debuff on the enemy side.