1. Preheat oven to 425 degrees Fahrenheit (220 degrees Celsius).
2. Spray one large and two small baking pans with cooking spray. Place sweet potato cubes in the large pan, and the mushrooms and onions in the two small pans. (Do not combine onions and mushrooms, as the juices from the mushrooms will prevent the onions from roasting properly.)
3. Drizzle all vegetables with oil and sprinkle with salt, tossing to coat. To ensure proper roasting, make sure the vegetables are not overcrowded.
4. Roast on the middle rack of your oven for 30 minutes, stirring once or twice during baking. Sweet potatoes may need an additional 10 minutes. Remove from oven when potato edges are browning, leaving oven on for the skewers (see below).