In a medium bowl, whisk together flour, oats, salt, cinnamon, and baking powder. Set aside.
In another bowl, cream together sugar and oil by hand.
Add in eggs one at a time and mix well. Stir in yogurt, applesauce and vanilla until well incorporated.
Gradually add dry ingredients to the wet ingredients and stir to combine. Do not over mix.
Drop muffin liners into muffin pan, and then fill 3/4 full with the batter. Bake at 425 for 3 minutes, and then turn the oven to 350 and bake for an additional 17-18 minutes. The muffins are done when a toothpick comes out with crumbs on it. Remove the muffins from the pan and cool.