Preheat the oven to 350°F (175°C).
Combine chicken, 2 tablespoons lime juice, 1/4 cup orange juice, sliced jalapeños, 4 minced garlic cloves, oregano, cumin, salt, pepper, and 1½ tablespoons oil in a large resealable bag or bowl; massage to coat.
Refrigerate the chicken to marinate for at least 20 minutes or up to 3 hours.
Heat the remaining 1½ tablespoons oil in an oven-safe skillet over medium-high heat until hot.
Sear the chicken in the hot skillet 2–3 minutes per side until golden brown.
Transfer the skillet to the oven (or move chicken to a baking sheet) and bake 10–15 minutes more, until the internal temperature reaches 165°F (74°C).
Remove chicken and let rest 5 minutes, then dice into bite-sized pieces.
Make the cilantro sauce by blending 1/2 cup Greek yogurt, 1/2 cup salsa verde, 1/2 cup cilantro, 1 tablespoon lime juice, and 1 clove garlic until smooth.
Heat 1 tablespoon oil in a skillet over high heat. Toast each tortilla 30–45 seconds per side until lightly browned, working in batches.
Assemble tacos: fill each tortilla with diced chicken, pickled red onion, quartered grape tomatoes, feta, a drizzle of cilantro sauce, smashed avocado, and chopped radishes; garnish with extra cilantro if desired.