There's a joke among my colleagues from when we were trying to set the rules for a friendly game: "No-rules conkers is a fistfight in the carpark."
My candidates for the name of a combined Cultivation & Odium:
Vendetta
Armageddon or Chaos
Rebellion or Riot
Fistfight in the Carpark
I subscribe to the idea that War and Science are the possible names for the other two combos. Thing is, without Honor involved you don't get structure. "Cultivation" does imply a certain amount of deliberateness or direction, but not rules. Rules are what make a war - not rules between opposing sides, but within a side. If you don't have structure, you don't have an army - just a mob.
Some candidates for cultivated wrath, destructive progression, or what have you, are out by virtue of already existing - Ruin and Calamity (not cosmere, but ruled out anyway) would work, but they're taken. I'd veer towards Tempest or similar for the idea of magnified destruction, but the storms are already a thing and (weirdly, I think) strongly associated with Honor.