In the bowl of a food processor, add the orange juice, lime juice, olive oil, garlic, jalapeño peppers, cilantro, oregano, paprika, cumin, salt, and pepper. Process into a smooth paste.
Place the skirt steak into a gallon size plastic bag. Pour the marinade over the steak. Seal the bag tightly. Toss and massage the steak to coat evenly with the marinade. Place the bag inside a baking dish or bowl in case it leaks and refrigerate for up to 2 hours.
Remove the steak from the fridge 30 minutes prior to grilling. Prepare your charcoal or preheat your gas grill so that it is medium-high heat. Coat the grill grates with vegetable oil before grilling.
Remove the steak from the marinade and wipe most of the marinade off with your hands. Place the steak on the grill and cook for approximately 3 minutes per side or until the internal temperature reaches 125°F when checked with a digital meat of thermometer.
Set the steak aside on a clean cutting board to rest while you prepare the taco ingredients.
Tacos
Prepare a platter of diced cucumbers, avocado slices, and shredded lettuce. Slice the skirt steak thinly against the grain and place this on the platter. Add the lime wedges to the perimeter of the platter.
Warm the tortillas for a few seconds on each side on the grill. Place them on the platter or in a basket. Serve the make-your-own tacos immediately.