Wipe fish with damp cloth and cut into serving-size pieces.
Combine lemon juice, wine, garlic, oregano, salt, pepper, and fennel.
Place fish in a plastic bag, pour in marinade, and twist-tie bag closed.
Chill for 1 to 2 hours, turning bag often.Lift fish from marinade and drain briefly (reserve marinade).
Place on a well-greased grill 4 to 6 inches above a solid bed of medium-glowing coals.
Cook, turning once, for 5 to 8 minutes on each side or until fish flakes readily when prodded in thickest portion with a fork.
As soon as fish goes on the grill, saute mushrooms in oil until limp (about 5 minutes).
If you use a heavy metal frying pan, you can cook mushrooms on grill over the coals.
Stir in reserved marinade and simmer for about 2 minutes.
Transfer cooked fish to a serving plate; top with mushroom sauce and sprinkle with green onion.