Rinse and drain quinoa 2-3 times to remove saporin (bitter coating); place drained quinoa in medium saucepan with water and chicken broth. Bring to a boil, then reduce heat to low and cook, covered, for 15 minutes. Turn heat off and let quinoa stand for 5 additional minutes, covered. Transfer to a large mixing bowl and add vinegar, 2 tablespoons extra virgin olive oil and oregano; set aside and let cool to room temperature.
Add tomatoes, bell pepper, cucumber, red onion, feta cheese, lemon juice, and remaining olive oil to quinoa. Toss well. Season to taste with salt and pepper.