Soak 8 wooden skewers in a large bowl of water for 10 minutes. Heat broiler.
Alternating, thread the fish, tomatoes, bell pepper, and mushrooms onto the skewers, ending each with a lime wedge.
Place the skewers on a rimmed baking sheet and toss with the oil, oregano, and ½ teaspoon salt.
Broil the skewers until the fish is cooked through and the vegetables are slightly charred, 3 to 4 minutes per side.