Good counters to AoE comps?
To counter an AOE comp, you must prey on their weakness of needing to teamfight.
If you run a split-push comp (see: Nidalee, Shen) or a poke comp (see: Kog'Maw, Xerath, Trundle) which both whittle down the opposing team without an actual 5v5, you completely shut down the main objective of an AOE comp.
If the above is not possible for some reason, champions that have good disengages are always a good option. The number 1 disengager in the game is of course, Janna. AOE knockbacks are incredibly effective in stopping champions like Kennen and Galio (see: Tristana, Lee Sin, Alistar).
A poke composition really helps counter aoe fests. Only ever initiate when the enemy are at a very low health from all of the harass you have given. You will always want one champ specifically picked to counter the AoE if you do get engaged.
Examples are:
Pick one champ like that can break initiates:
Trundle, Anivia, Janna, Lee sin.
Then poke champs.
Nidalee, Ezreal, Ahri etc. You know the score.