In a small saucepan, cook juice over high heat until reduced to 2 tbsp., about 5 minutes; let cool. In a small bowl, whisk together juice, oil, vinegar, salt, and chopped oregano.
Cut off ends and outer white membrane from oranges; slice into rounds. In a bowl, gently toss oranges, radicchio, onion, and oregano leaves with dressing to coat.
Note: Nutritional analysis is per serving.