Bring a large pot of salted water to a boil over medium heat and drop in the green beans; cook until slightly tender, but still crisp, 8 to 10 minutes. Immediately drain the green beans and plunge into ice water to stop the beans from cooking further. Drain the beans and place them in a shallow serving dish.
Heat the olive oil in a skillet over medium heat. Cook garlic in the oil for about 30 seconds. Remove the skillet from the heat. Stir in the olives, tomatoes, vinegar, oregano, salt, and pepper. Pour mixture over green beans. Toss together until beans are evenly coated. Sprinkle feta cheese over the top and garnish with oregano sprigs. Chill at least 3 hours before serving.