Whisk the vegetable oil, soy sauce, lemon juice, mustard, Worcestershire sauce, garlic, black pepper, and salt together in a bowl; pour into a resealable plastic bag. Add the beef, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator 8 hours or overnight.
Add the mushrooms to the bag, coat with the marinade, squeeze out excess air, and reseal the bag; marinate in the refrigerator another 8 hours.
Preheat an outdoor grill for high heat, and lightly oil the grate.
Remove the beef and mushrooms from the marinade, shaking off any excess liquid. Pour the marinade into a small saucepan and bring to a boil over high heat. Reduce heat to medium-low, and simmer for 10 minutes; set aside for basting.
Thread pieces of green bell pepper, beef, red bell pepper, mushroom, and onion onto metal skewers, repeating until all ingredients are skewered.
Cook the skewers on the preheated grill, turning frequently and brushing generously with the reserved marinade until nicely browned on all sides and the meat is no longer pink in the center, about 15 minutes.
