[Archonsod]

I've never had a problem with the Oni Kings. Usually, keeping a mass of Dai Oni together throwing fireballs & poison at approaching troops keeps them out of combat (the enemy tend to retreat before they reach the demons).
Priests could be problematic, but again you can mix in non demonic troops (such as a bunch of bandits scripted to fire at the rear, hopefully killing the priest quite quickly).
One possibility would be to use stealth armies of bandits scripted to loose off a few volleys towards the enemies' rear and retreat. You could then ambush priest heavy armies and try to remove the priests, before delivering the killing blow with the demons.