Barbarian magic suppression skills...

Regarding other factions... I don't use any filler units. I prefer to take Barbarian Luck and find artifacts (which isn't that difficult).
I calculate my skills in such a way that there's no room for filler units.

Dungeon has a universal and effective weapon against which resistances are useless - Vampirism, I especially recommend it on alternate griffons (it really shines in duels against warriors), and against orcs, it also deals -90 rage for each Drain. And Unsuppressed Light, as HumanSt said, is also a powerful tool: Defense +12, Attack +12, initiative of 1.4, maximum damage (griffons, archers, seraphs), all this for 2 standard turns and 40 mana.
Haven, as paradoxical as it may sound, should focus on 2 magic types against orcs, and there are also Twilight and Fallen Knight. Trying to overwhelm a barbarian with brute force is suicide, but with magical support, it's quite possible.