Preheat the oven to 350 degrees F and move a rack to the middle of the oven. Coat a 9-by-13-inch baking dish with cooking spray.
In a large bowl add the strawberries, blackberries, blueberries, raspberries, granulated sugar, cornstarch and cinnamon. Mix until the berries are evenly coated, and then pour into the prepared baking dish.
Combine the oats, flour, brown sugar, butter and salt in a medium bowl. Work the mixture with a pastry cutter or your hands until it resembles coarse meal. Spread the topping evenly over the berries, then bake until the topping is golden brown and the filling bubbles up at the sides, 45 minutes.
Cool for 10 minutes before serving.
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