Preheat oven to 425 degrees F (220 degrees C). Grease muffin cups or line with paper muffin liners.
Mix flour, oats, sugar, baking powder, baking soda, and salt together in a bowl. Combine milk, vegetable oil, egg, and vanilla extract in a separate bowl.
Stir milk mixture into flour mixture until batter is combined. Fold in strawberries and blueberries. Spoon batter into prepared muffin pan until full.
Bake in preheated oven until a toothpick inserted into the center comes out clean, 18 to 22 minutes.
