Crumble Skillet Cornbread into a large bowl. Add breadcrumbs and next 7 ingredients; stir well. Cover and let stand at room temperature 8 hours.
Place chicken gizzards in a large saucepan. Cover with water; add 2 stalks celery and next 4 ingredients. Bring to a boil. Reduce heat; simmer, uncovered, 20 minutes.
Add chicken livers to saucepan; simmer 15 additional minutes or until tender. Drain, reserving 3 1/2 cups cooking liquid. Reserve gizzards and livers for giblet gravy, if desired.
Drain oysters, reserving liquid. Combine eggs, reserved cooking liquid, and reserved oyster liquid; add to cornbread mixture (dressing will be very moist).
Spoon cornbread mixture into a greased 13" x 9" x 2" baking dish. Push oysters gently and evenly into cornbread mixture. Bake dressing at 350° for 1 hour.