Preheat the oven to 350. Spray a 9x13 baking dish.
In a mixing bowl, whisk together the eggs, oil, milk, then stir in the sugar, quick cooking oats and rolled oats. Stir to combine, then add the flour, baking powder and salt. Stir to combine, then fold in the mashed bananas and chopped strawberries.
Transfer the batter into the prepared baking dish, then sprinkle the turbinado or brown sugar over the top.
Bake in the preheated oven for 30 to 35 minutes, or until toothpick comes out clean in the middle.
Serve Strawberry Banana Baked Oatmeal with milk, cream, or yogurt.