In a large, shallow bowl, mix oil, oregano, vinegar, and garlic. Add steak and toss to fully coat. Cover with plastic wrap and marinate at least 30 minutes or up to 4 hours, flipping the steak halfway through. Remove from fridge at least 1 hour prior to cooking.

Preheat grill, grill pan, or large cast iron skillet, to medium-high heat. Season both sides of steak generously with salt and pepper. Let excess marinade drip off steak and transfer steak to pan. Cook until golden brown, 5-7 minutes per side for medium rare.

Transfer steak to a cutting board and allow meat to rest for 5 minutes. Slice steak into 1/2-inch pieces across the grain.

Assemble gyros by stuffing pita halves with lettuce, onions, tomatoes, and steak. Drizzle with tzatziki sauce and serve immediately.