Preheat oven to 325 degrees. Cream butter. Gradually add sugars, beating well until creamy. Add egg and beat well. Add oil and vanilla, mixing well.
Combine flour, soda, and salt. Add to creamed mixture mixing well. Stir in oats and remaining ingredients.
Shape dough into 1-inch balls (makes about 10 dozen!). Place on parchment-lined cookie sheets about 2 inches apart and flatten slightly using a fork. Bake for about 15 minutes. Cool slightly on pan then remove to wire rack to cool completely.