Place barley, water and 1 teaspoon salt in medium saucepan. Bring to a boil.
Reduce heat to low, cover and cook 45 minutes or until barley is tender and liquid is absorbed.
Combine olive oil, lemon juice, vinegar, oregano and ¼ teaspoon salt; pour over hot cooked barley. Cool to room temperature.
Gently stir in onions, parsley, tomatoes, bell pepper and cheese. Serve salad chilled or at room temperature on lettuce-lined plates.
Garnish each serving with tomato wedges or lemon slices, if desired.