In a medium bowl, stir together the sugar, milk, oil, egg and vanilla. In a separate bowl, combine the flour, baking powder, baking soda and salt. Add the dry ingredients to the wet ingredients and stir until just combined.
In a small bowl, toss together the strawberries and the 2 tablespoons of flour to coat the strawberries. Fold the floured strawberries gently into the batter.
Pour the bread batter into a greased 9"x5" bread pan. Bake at 350° degrees for 55-60 minutes or until a toothpick comes out clean. Allow the bread to cool for 10 minutes, then remove the bread to a wire rack to cool completely.
Combine the powdered sugar, milk, diced strawberries and extract in a small bowl. Mix until it is smooth.
Once the bread is cool, spread the glaze on top of the bread. Slice and serve.