Whisk together 3 tablespoons of the oil, orange juice, garlic and oregano in a baking dish, add the pork and turn to coat. Cover and marinate in the refrigerator for at least 1 hour and up to 4 hours.
Heat the grill to high or a nonstick saute pan with a few tablespoons of canola oil over medium-high heat on the stove.
Remove the pork from the marinade and place on the grill. Grill until golden brown and slightly charred and an instant-read thermometer inserted into the center of the meat registers 150 degrees F, about 12 to 15 minutes. Remove from the grill and let rest 5 minutes before slicing into 1/4-inch thick slices.
Reduce the heat of the grill to medium. Place the tortillas on the grill and grill for approximately 10 seconds per side to make pliable. Lay the tortillas on a flat surface. Divide the ingredients evenly over 1 half of each tortilla. Start with 1 slice of the cheese, followed by the ham then a few slices of the pork, a few slices of the jalapenos and another slice of the cheese. Fold the top of the tortilla over the ingredients and press on it. Brush the tops of the tortillas with some of the remaining oil and place on the grill, oil-side down and grill until lightly golden brown, pressing on the tortillas to flatten, 3 to 4 minutes. Brush the tops of the tortillas with oil, flip over and continue grilling, pressing down on the tortillas until golden brown and the cheese has melted.