Fill eight tall glasses (at least 12 oz.) with ice cubes. Rinse four oranges and cut a 1/4-inch crosswise slice from the middle of each. Cut each slice in half to form two half-moons. Squeeze juice from one of each of the eight remaining orange halves into each ice-filled glass. Pour 1/4 cup (2 oz.) Campari into each glass. Fill glasses with club soda and garnish rim of each glass with a half-slice of orange. Stir before drinking.