Thinly slice skirt steak or flank steak against the grain into ½ inch pieces. Place steak in large bowl or Ziploc bag. Set aside.
Combine soy sauce, lime juice, 1 tablespoon vegetable oil, garlic, chili powder, cumin and oregano. Add to bowl or Ziploc bag with steak. Marinate in the refrigerator for 1-2 hours.
Heat remaining 1 tablespoon oil in a large skillet over medium high heat. Add steak and marinade, and cook, stirring often, until steak has browned and marinade has reduced, about 5-6 minutes, or until desired doneness. For medium rare, cook to an internal temperature of 130-134°F as indicated by an instant read thermometer.
Serve steak in tortillas, topped with onion, cilantro and salsa.