Minor correction: Rotom can be caught before Postgame. I got one from a trash can in the Lost Hotel [I think?] well before I beat the E4.
I used Charizard X, Honedge, Aurorus, Vivillon, Goodra, Chestnaught, Xerneas, and Dunsparce. Dunsparce and Chestnaught weren't used all the way through...