Make the marinade: Combine oil, red vine vinegar, lime juice, orange juice, water, garlic, salt, pepper, cumin, chili powder, oregano and cilantro in a large bowl.
Add chicken to the bowl of marinade and place in the fridge for at least 4 hours or overnight.
Heat your barbecue to medium heat. Grill chicken on the barbecue for about 5 minutes with the barbecue lid shut. Flip chicken over and cook for another 5 minutes. Chicken should have nice grill marks on both sides and will be cooked all the way through.
Transfer chicken to a cutting board and chop into bite size pieces.
Heat up your corn tortillas on the barbecue for about 30 seconds to 1 minute on each side.
Serve your tacos with avocado salsa verde, sliced radishes, cilantro and onion. Enjoy!