For meat: combine steak and next six ingredients in a heavy ziploc bag, squeezing the limes in and adding peels to the bag. Seal and massage to combine and cover meat. Allow to marinate for at least one but up to four hours. Remove from marinade and grill over medium high heat for approximately 15 minutes, flipping several times. Allow to rest for 10 minutes and slice thinly against the grain.
For pickles: Slice radishes and red onion and put in mason jar or similar tightly lidded container. Combine next five ingredients and bring to a boil just long enough to dissolve sugar. Off heat, stir in vegetable oil. Pour over radishes and onion in jar, shake to combine, and let marinate, optimally for 24 hours.
For sauce: combine parsley, oregano, garlic, salt, and peppers in a food processor and pulse until finely chopped. Stream in oil until emulsified.
To serve: lightly grill tortillas. Place several strips of steak in each tortilla, scatter with 1/2 cup or so of pickles and about a tablespoon of sauce.