Drain oysters. Blot oysters dry on paper toweling.
Place flour and cracker crumbs on separate sheets of wax paper. Beat eggs slightly in small bowl.
Dredge oysters in flour; dip into egg, then in crumbs, pressing crumbs to adhere. Place on wax-paper-lined baking sheet.
Heat 2 tablespoons butter and 1 tablespoon oil in large, heavy skillet over medium-high heat just until butter is melted. Add a third of the oysters, and sauté for 2 minutes until golden brown. Turn over, and sauté for another 2 minutes. Remove to a paper-towel-lined tray. Empty skillet and wipe clean. Repeat frying in 2 batches with the remaining oysters. Makes 8 servings.