Cut cactus paddles into 3/4-inch pieces. Rinse 2 or 3 times under running water. Place cactus and water to cover in medium saucepan. Bring to boil. Reduce heat to low; simmer, uncovered 20 to 25 minutes or until tender-crisp. Drain. Cool slightly.
Place cactus in large bowl. Add tomatoes, cheese, onion, cilantro, oregano, salt and pepper; toss lightly. Add lime juice; toss to coat evenly. Cover.
Refrigerate at least 1 hour to blend flavors.