Get the grill ready (or turn on the indoor grill to high).
Chop the protein (I used chicken into bite-size cubes (large enough to go on the skewer).
Combine the oil, vinegar, 1/4 cup of orange juice, cumin, 1 1/2 tsp oregano, and 1 tsp salt in a large bowl. Whisk together thoroughly and add the chicken cubes to the bowl. With your hands, mix the chicken cubes into the marinade.
Cut the peppers, squash and onions into bite size pieces, keeping in mind that they need to fit on the skewer.
Skewer the chicken pieces, the vegetables and tomatoes, alternating pieces for color. If you have a group of people, let everyone skewer their own.
Place the skewers on the grill over medium heat for 5-7 minutes, flip and grill for an additional 5-7 minutes. I did this inside with a pannini maker instead of outside on the grill. Since the pannini maker grills top and bottom at the same time, it only took about 7-10 minutes and no flipping.
To make the dipping sauce:
In a medium size bowl combine the 1/2 cup mayonaise, 1 Tbsp orange juice, 2 tsp lime juice, 1 tsp mexican oregano, 1 Tbsp minced red onion, 1-2 Tbsp minced cilantro, 1/2 tsp salt, and 1/2 to 1 tsp chile spice. Whisk together until thoroughly combined.
Serve the skewers on a large plate with the dipping sauce and enjoy!