Heat oven to 400° F. Combine the tomatoes, Feta, 2 tablespoons of the oil, and ¼ teaspoon black pepper in a medium bowl.
Arrange the bell peppers, cut-side up, in a 9-by-13-inch baking dish. Fill the peppers with the tomato mixture, dividing evenly. Add 1 cup water to the baking dish and tightly cover the dish with foil.
Bake until the bell peppers are beginning to soften, 40 to 50 minutes. Uncover the dish and bake until the bell peppers are soft and the tomatoes and Feta are beginning to brown, 15 to 20 minutes more.
Meanwhile, cook the barley according to the package directions. Toss with the remaining 2 tablespoons of oil and ½ teaspoon each salt and black pepper.
Serve the peppers over the barley. Sprinkle with oregano.