Yes, storm is a big pain for devils (and vamps) but if you expect and prepare for the storm, devils can still be quite effective. Even trailing in research you should be able to bring some spells of your own at the point storm is in 'every battle'. The nice thing about having groups of devils spawning every turn (and immortal vamps of course) is it's unlikely you can manage to loose so many in one surprise to set you back too much.
Option 1: Kill the guy with the storm staff/A gems. Disease demons, earth attacks, mind hunts, manifestations, slayers. You can also stick black hearts on vamp lords for heavier duty assassins - raise skeletons, hellbind heart, life for life...
Option 2: Darkness. Under darkness & storm you won't be taking any significant archer fire and it takes a hell of a lot of mages to do much damage. Then, of course, you've got devils fighting under darkness once they close to melee, which is pretty terrifying.
Option 3: Horrors fly in storms. Use your devils to cut off the retreat rather than fighting the guys dropping the storm, then use the tactics I outlined above. Bonus: enemy mages will have a harder time targeting the horrors!
Option 4: If you've managed to get some storm demons they do quite well in storms - and it doesn't take many. A dozen can lay down some serious hurt against armies that don't bring a bunch of chaff. They've got storm flight as well if you see an opportunity to jump back and kill guys who thought they were protected from fliers, or just bask in the fact that you've brought the only effective ranged weapons to the fight and let the enemy run across the field to your devils/heavy infantry getting pounded by AN lightning. Hey, who thought they needed lighting resistance to fight Abysia?
Option 5: Precision 100 spells. Leech, enslave mind, soul slay, life for life, incinerate, bloodletting, fire storm, drain life, prison of fire, hydrophobia, heat from hell, inner furnace, curse of stones, etc. etc.
Option 6: Use all of the above together.
You can't really expect to take out multifaceted armies supported by battlefield enchantments with just flying one unit type in and attacking. If your opponent is doing things to counter what you're fielding....you need to do the same thing!