Preheat the oven to 350°. In a shallow, nonreactive dish, mix together the lime juice and chili powder. Cut the steak crosswise into 4 equal pieces and place in the dish, turning to coat. Marinate at room temperature for 15 minutes, or cover and refrigerate for up to 4 hours. Wrap the tortillas in foil and warm in the oven for 10 minutes.
Meanwhile, in a medium bowl, combine the tomatoes, corn, onion, cilantro and vinegar. Set the salsa aside.
In a large skillet, heat the oil over medium-high heat. Season the steak with salt and pepper and add to the skillet without crowding the pan. Cook until browned on the outside and pink in the center, turning once, 6 to 8 minutes total. Transfer to a cutting board and let rest for 5 minutes. Cut on the diagonal against the grain into 1/4-inch-thick slices.
Season the salsa with salt and pepper. Lay a tortilla flat on a work surface. Place one quarter of the steak in the center and, using a slotted spoon, top with about 1/2 cup salsa. Tuck in the sides and fold the tortilla to close. Serve with extra salsa on the side.