Heat oven to 375°F. Line 12 muffin cups with paper baking cups. In medium bowl, combine sugar, oil and eggs; blend well. Stir in bananas and vanilla.
Lightly spoon flour into measuring cup; level off. Add flour, baking soda and salt to sugar mixture; stir just until combined. Stir in strawberries. Spoon batter evenly into paper-lined muffin cups.
Bake at 375°F. for 17 to 21 minutes or until toothpick inserted in center comes out clean. Immediately remove from muffin cups. Serve warm or cool.