Preheat oven to 425°F (220°C). Line a large baking sheet with parchment paper or lightly grease it.
In a medium bowl, combine shredded chicken, softened cream cheese, salsa verde, shredded cheese, cumin, chili powder, garlic powder, onion powder, salt, and cilantro. Mix until everything is evenly incorporated and the cream cheese is fully blended.
Wrap a stack of 4-5 corn tortillas in a damp paper towel and microwave on high for 30-45 seconds. They should be pliable and warm. Keep them covered while you work.
Place about 2 tablespoons of filling in a line across the lower third of each tortilla. Roll up tightly and place seam-side down on the hot baking sheet. Repeat with remaining tortillas and filling, working in batches.
Lightly brush the tops and sides of the rolled taquitos with oil. Bake for 15-20 minutes, turning once halfway through, until golden and crispy. Ensure the filling reaches an internal temperature of 165°F (74°C) for food safety.
While the taquitos bake, stir together crema and lime juice. Once taquitos are done, let them cool 2 minutes, then transfer to a platter. Drizzle with lime crema, sprinkle with queso fresco and extra cilantro, and serve with salsa roja.