Preheat the oven to 350 degrees F. Lightly oil and flour 3 (9 by 1 1/2-inch round) cake pans.
In a medium sized bowl, sift together flour, baking soda, cocoa powder, and salt. Set aside. In a large mixing bowl cream together the sugar and vegetable oil. Add eggs one at a time, mixing until they are well incorporated. Add the vanilla extract, mix. Add the distilled vinegar, mix. Add the food coloring, mix. Mix the dry ingredients into the butter and oil mixture, alternating with milk and ending with dry (dry, milk, dry, milk, dry). Mix batter for 1 minute more.
Divide batter evenly among the cake pans and bake for 40-45 minutes, rotating halfway through.
For the Frosting:
Cream together cream cheese, vanilla and sugar in a bowl. Spread over all three cooled cakes, stack, slice, and serve.