In saucepan of boiling salted water, cook barley until tender, about 20 minutes. Drain and rinse under cold water; drain well. Let stand for 10 minutes to dry. Transfer to large bowl.
Meanwhile, in a separate saucepan, bring 1 1/2 cups salted water to boil. Add rice; cover, reduce heat, and simmer until tender and no liquid remains, about 15 minutes. Let stand for 5 minutes. Add to barley mixture; let cool.
Cut tomatoes in half; add to barley mixture. Cut onion, red pepper, and cucumber into 1 inch chunks, add to barley, tossing to combine.
Dressing: In a large bowl, whisk together oil, lemon juice, oregano, salt, and pepper, pour over salad and toss to coat. Refrigerate for 30 minutes up to 24 hours.