Preheat oven to 350°F. Line muffin tin with paper liners (or grease).
In the bowl of a stand mixer, or a large bowl with a hand mixer, beat butter and sugar together until fluffy and light in color. Add the egg and vanilla and mix for 1 minute. Add in bananas and mix for 1-2 minutes, until well combined.
Sift flour, baking powder, baking soda, and salt into the bowl, and mix briefly, until just combined.
Fold in oats and strawberries.
Divide batter evenly between muffin wells (using a cookie scoop).
Bake for 18-20 minutes, or until a toothpick stuck in the center comes out clean.