Light a charcoal grill. In a small bowl, whisk the olive oil with the lemon juice, red wine vinegar, mustard and oregano and season with salt and pepper. Transfer half of the dressing to a large bowl. Add the zucchini, onion, red bell pepper, mushrooms, asparagus and scallions. Season the vegetables with salt and pepper and toss.
In a perforated grill pan, grill the vegetables over high heat, tossing, until charred in spots, 10 minutes; return to the bowl, add the remaining dressing and toss.
Season the steaks generously with salt and pepper. Grill the steaks over high heat, turning occasionally, about 11 minutes for medium-rare meat. Transfer the steaks to a carving board and let rest for 5 minutes. Slice the meat from the bones and serve with the grilled vegetables.