Cream butter in a large mixing bowl; gradually add sugar, beating well. Add eggs and vanilla, beating well.
Sift together flour, soda, and salt in a small mixing bowl; stir into creamed mixture, mixing well. Stir in oats and walnuts.
Drop by teaspoonfuls 3 inches apart onto greased cookie sheets. Bake at 375° for 10 minutes or until golden brown. Remove from cookie sheets, and cool on wire racks.
Note: One cup flaked coconut may be added to batter.