Cut the steak: Pat steak dry, then cut into even 1¼-inch cubes so the pieces cook at the same pace.
Make the marinade: Whisk together olive oil, soy sauce, Worcestershire sauce, lemon juice, vinegar, honey, garlic, Dijon, smoked paprika, oregano, and black pepper. Reserve a few tablespoons before adding raw beef if you want extra brushing sauce.
Marinate the beef: Add steak cubes to a zip-top bag or shallow container. Pour in the marinade, coat well, and refrigerate for at least 1 hour, or 3–6 hours for deeper flavor.
Prep the vegetables: Cut peppers, onions, and mushrooms into pieces close to the steak size. Toss with olive oil, salt, and pepper.
Thread the kabobs: Alternate steak and vegetables on skewers, leaving small gaps between pieces so they sear instead of steam.
Grill and rest: Grill over medium-high heat, about 400–425°F, for 8–15 minutes, turning every 2–3 minutes. Cook to your preferred doneness, then rest for 5 minutes before serving.