Preheat oven to 400 degrees F (200 degrees C). Grease or line 12 muffin cups with paper liners.
Beat sugar and oil together in a bowl using an electric mixer until smooth, about 2 minutes. Beat eggs and vanilla extract into sugar mixture until smooth, about 1 minute.
Whisk flour, cinnamon, baking soda, and salt together in a separate bowl; beat into sugar mixture until batter is just combined. Fold apples and walnuts into batter; spoon into muffin cups.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes.
