Seasoning the steaks: Place the beef in a bowl, and add onion, oregano, pepper, vinegar, lime juice, Worcestershire sauce, and salt.Marinate for an hour at room temperature.
Cooking the steaks: Once an hour has passed, separate the meat and onions from the marinade liquid. Reserve the liquid and the onions separately. Lightly pat dry the beef slices using a paper towel.Heat the oil over high heat in a large non-stick pan. Add the beef slices (careful with splatters), Cook for half a minute, turn and cook the other side for another 30 seconds. Remove them from the pan.
Cooking the onions: Add the onions to the pan and lower the heat to low. Cook and stir until the onions become translucent.Once the onions are cooked, increase the heat to medium, and add the liquid from the marinade and simmer until the liquid has reduced to half. Try and season with salt to taste if you find it necessary. Remove from the heat.
Serving: Serve the steak with the onions. See serving suggestions above recipe.