Beat the eggs in a large mixing bowl. Add vegetable oil and the cream cheese to the eggs. Mix until creamy.
In another bowl, sift together sugar, flour, cocoa, baking powder and salt. Add these dry ingredients to the egg mixture. Stir the batter until smooth and pudding-like, adding small amounts of milk as necessary. Add in the vanilla and stir. Finally, add the soda water and walnuts. Stir until well blended.
Pour batter into a 9 x 13 inch pan that has been coated with cooking spray. Bake at 350 degrees for about 45 minutes, or until toothpick inserted in center comes out clean. Cool.