Thaw salmon, if frozen. Set aside. Cook carrots, covered, in a saucepan in a small amount of boiling water for 2 minutes. Drain and set aside. Fold four 24x18-inch pieces of heavy foil in half to make 18x12-inch pieces.
Combine carrots, mushrooms, onions, orange peel, oregano, garlic, the 1/4 teaspoon salt, and the 1/4 teaspoon pepper in a large bowl; toss gently.
Divide vegetables among the four pieces of foil, placing in center. Top each with 1 salmon fillet; drizzle with 1 1/2 teaspoons oil. Sprinkle each lightly with additional salt and pepper; top with orange slices. Bring together 2 opposite edges of foil; seal with a double fold. Fold remaining edges to enclose the mixture, leaving space for steam to build.
Grill the packet on the rack of an uncovered grill directly over medium heat for 15 to 20 minutes or until carrots are tender and fish flakes easily with a fork. If desired, garnish with fresh oregano sprigs. Makes 4 servings.