Preheat a grill on medium heat or the oven broiler on high.
Mix the orange juice, lime juice, garlic, and ginger in a bowl and add in the meat. Season with salt and pepper. Set aside. Soak the wooden skewers in water for 10 minutes.
Thread the steak, pineapple, bell peppers, onion, and mushrooms alternately onto the skewers.
Grill or broil the skewers, turning every 2 - 3 minutes until the vegetables are soft and everything has a nice char. Using a thermometer cook to your desire temperature of the meat (see below). Then serve.