Preheat oven to 350°F (175°C). Line a 12-cup muffin tin or lightly grease it.
In a large bowl, whisk mashed bananas, applesauce, eggs, brown sugar, and vanilla.
Add oats, flour, baking soda, baking powder, and salt. Mix until just combined.
Gently fold in berries and walnuts.
Divide batter evenly into muffin cups, filling almost to the top.
Bake for 15–18 minutes until centers are set and edges are lightly golden.
Cool for 5 minutes in the pan, then transfer to a wire rack.
These Mixed Berry Baked Oatmeal Muffins are best enjoyed slightly warm or fully cooled.