Preheat oven to 350 F. Coat an 8 x 4 inch loaf pan with cooking spray or line with foil and set aside.
Beat sugar with eggs in a large bowl until mixture is thick and pale. In a separate bowl, combine flaxseed meal, flours, baking powder, baking soda, and salt. Stir to combine. In a third bowl, combine the soy milk, applesauce, and vanilla.
Alternate adding the flour mixture and the soymilk mixture to the egg mixture, beginning and ending with the flour mixture. Stir in the strawberries and banana.4. Pour batter into prepared pan. Bake at 350 F for 50-55 minutes or until an inserted toothpick comes out clean.
Cool in pan, on a wire rack, for 5-10 minutes before removing loaf from pan and cooling completely on a wire rack .