Combine the first 6 ingredients in a large bowl, and stir well. Add squashes, parsnip, and oil, tossing to coat. Spoon squash mixture into a 2-quart casserole coated with cooking spray. Cover and bake at 325° for 1 1/2 hours. Sprinkle with cheese, and bake, uncovered, an additional 15 minutes. Garnish with oregano, if desired.
Note: Use any combination of winter squash to equal 6 cups, if desired.