Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish.
Mix milk and vinegar together in a bowl.
Stir white sugar, vegetable oil, milk mixture, brown sugar, and butter together in a bowl; add baking soda and baking powder and stir. Mix oats into sugar mixture. Stir flour, 1 cup at a time, into sugar-oat mixture until batter is evenly combined; fold in bananas. Pour batter into the prepared baking dish.
Bake in the preheated oven until golden brown and a toothpick inserted in the center comes out clean, about 45 minutes.