Cook pasta according to package directions. Drain in a colander. Rinse with cold water; drain again.
In a large bowl toss together the cooked pasta, tomatoes, cucumber, green onions, and olives.
In a screw-top jar combine the olive oil, lemon juice, basil, the 2 tablespoons oregano, anchovy paste (if using), garlic, salt, and pepper. Cover and shake well. Drizzle over pasta mixture; toss to coat.
Cover and chill in refrigerator for as least 2 hours or up to 24 hours. To serve, add feta cheese; toss. Sprinkle fresh oregano leaves. Makes 12 to 16 side-dish servings.