Combine oil, lemon juice, oregano, rosemary, salt, pepper, and garlic.
Heat an outdoor gas grill, or prepare coals for a charcoal grill for direct grilling over medium-high heat. Brush the cooking grates clean and oil the grill rack. Brush vegetables with oregano-oil mixture and grill until just softened and lightly charred, about 12 minutes, turning several times. Remove to a platter; loosely cover to keep warm.
Brush cooking grates clean and re-oil grill rack. Brush fillets with more oregano oil and grill 10 minutes, turning once, or until just opaque but still moist in the center. Serve drizzled with extra-virgin olive oil, if desired, and with lemon wedges.