Is a 2 quart baking dish approximately 13x8 oval or larger?

Take the pan you are considering to use and pour 2 quarts of water in it. If it holds fine, you are okay. If it overflows onto the floor...

Your 13 x 8 oval should be fine. I wouldn't go larger.

By way of comparison, 2 quarts fills a standard 8x8 pan (64 square inches) almost to the top and a standard 9x9 pan (81 square inches) comfortably. A 9x13 pan (117 square inches) holds 3 quarts comfortably.

The following are all 2 qt dishes: 8x8x2 9x9x1.5 and 7x11x2