Preheat a grill to medium-high.
Rinse the fish well under cold running water and pat dry with paper towels. Season the fish all over inside and out with salt and freshly ground black pepper. Brush each fish generously with 1/2 tablespoon of the olive oil and place directly on the grill. Cook, turning occasionally and coating with more olive oil if necessary, until flesh flakes easily and fish is cooked through, about 6 minutes per side. Place fish on a platter. Meanwhile, in a small bowl combine remaining olive oil with the lemon juice, parsley, and oregano. Season, to taste, with salt and pepper. Serve fish drizzled with the olive oil-lemon mixture.