Layer half the halibut slices in a 9x13-inch baking dish. Mix sour cream and mayonnaise in a small bowl until smooth; spread half the sour cream mixture over halibut. Spread mushroom slices on top, followed by a layer of half the onion slices and half the Cheddar cheese. Repeat layers of halibut, sour cream mixture, onion, and Cheddar cheese. Sprinkle with saltine crackers.
Bake until crackers are browned and fish is easily flaked with a fork, 35 to 40 minutes.