Preheat oven to 325 degrees F. Grease the inside of an 8 x 4½ inch loaf pan with vegetable oil and set aside.
Using an electric mixer, beat together oil, eggs, vinegar and vanilla in a large bowl.
In a separate bowl, place sugar, nutmeg, baking powder, salt, flours, oats and flax seeds. Stir to combine.
Make a well in the center of the dry ingredients and pour in egg mixture. Beat just until dry ingredients are moistened, about 15 seconds.
Add strawberries and walnuts, mixing briefly just to combine. Pour into prepared loaf pan and bake for 50 minutes or until a toothpick inserted into the center comes out clean.
Remove from heat and let cool on a wire rack before slicing. Serve warm or at room temperature.