I am no expert team fighter but from what I understand (and have seen) all effective team fight victories are won by not fighting until someone on the enemy side makes a mistake (gets too close, initiates poorly, etc.), or you've got a clear strategy and initiation plan, and are certain you're going to just cut through them.
In short: Counter it the same way you counter any team fight... don't engage until engaging equals victory: Make them waste their ults. All AoE abilities, no matter how powerful, are limited by their range. Morgana's is particularly easy to avoid. Not too familiar with Oriana or Jarvan's though. The single biggest problem I see in team fights, is people have this sense they have to charge and attack. No, you don't. And except in certain situations, keeping all your team alive and at full health for the right moment is more important than defending some objective. Just hang back until they mess up, try to engineer a situation where they're liable to, and then capitalize on it.