For rub, stir together paprika, sugar, 1 tsp. salt, and 1/2 tsp. pepper. Coat steaks with 1 Tbsp. oil; rub mixture on both sides. Let stand at room temperature 30 minutes.
For charcoal grill, arrange medium-hot coals on one side of grill. Place steaks on rack directly over coals. Cover and lightly sear on both sides, 5 to 6 minutes. Move to unheated side of grill. Cover and grill 4 to 5 minutes more for medium rare (145 degrees F). Remove; let stand 5 minutes. Grill lemon halves, cut side down, directly over coals, 2 minutes. (For gas grill, preheat grill. Adjust heat for indirect cooking. Grill as above.)
Serve with lemons, avocado, and feta. Sprinkle oregano and lemon peel; drizzle remaining oil. Serves 8.