Preheat oven to 350F. Spray disposable baking pans with nonstick spray.
Whisk together flour, baking powder, and salt in a large bowl.
Combine sugar, oil, eggs, and vanilla extract in another bowl. Mix with an electric mixer on medium speed until ingredients are just combined.
Add half of flour mixture and half of milk to sugar mixture. Mix well. Repeat with second half of flour mixture and milk.
Divide batter evenly into 7 bowls. When adding food coloring to each bowl, start out with about 1/4 - 1/2 tsp. Add more as necessary. Pour cake batter into prepared pans. Bake in batches of two or three for 10-12 minutes, or until center has set and edges of cake slightly pull away from the pan. Let cake layers cool completely before frosting.