Preheat oven to 350 degrees F (175 degrees C). Grease 2 muffin tins with cooking spray.
Mix soy milk, applesauce, vinegar, and vanilla extract together in a bowl.
Sift white whole wheat flour and whole wheat flour together into a separate bowl. Add oats, baking soda, and salt in a separate bowl. Mix in soy milk mixture until smooth. Let batter sit for 5 minutes.
Fold strawberries into the batter. Fill muffin tins 2/3 full of batter.
Bake in the preheated oven until muffin tops are brown and sides pull away from the tin, 30 to 40 minutes.