In a medium bowl combine 1 cup of the chopped onion, 1/4 cup cilantro, olive oil, 3 tablespoons lime juice, orange juice, garlic, and oregano until combined.
Sprinkle fish with salt and pepper.
Spread half of the onion mixture in the bottom of a baking dish. Arrange fish atop onion mixture. Spoon remaining onion mixture over fish. Cover and chill for 30 minutes. Turn fish; cover and chill for 30 minutes longer.
Whisk mayonnaise, milk, and remaining 2 tablespoons of lime juice in a small bowl, set aside.
Using a silicone grill brush, brush grill grate with olive oil; turn grill on to medium-high heat. Grill fish with some marinade still clinging to it, 3 to 5 minutes per side, until fish easily flakes. Check that it is cooked with the help of your thermopro thermometer. The internal temperature should be 145° F (63° C). Grill tortillas until slightly charred, about 10 seconds per side.
Coarsely chop the grilled tilapia; place on a platter.
Serve with lime mayonnaise, tortillas, remaining 1 cup chopped onion, remaining 1/4 cup cilantro, avocados, cabbage, salsa verde or pico de gallo and lime wedges.