In a large mixing bowl, combine the shredded chicken, cheddar cheese, cream cheese, garlic powder, onion powder, chili powder, salt, and pepper. Stir until well mixed.
Lay a tortilla flat on a clean surface. Place about 2 tablespoons of the chicken filling towards one edge of the tortilla. Roll it tightly, tucking in the sides as you go, to form a snug taquito. Repeat with the remaining tortillas and filling.
In a deep skillet, pour in the vegetable oil and heat over medium-high heat until hot (about 350°F or 175°C).
Carefully add the taquitos to the hot oil in batches, making sure not to overcrowd the pan. Fry them for about 2-3 minutes on each side or until they are golden brown and crispy. Use tongs to flip them halfway through.
Once crispy, remove the taquitos from the oil and place them on a plate lined with paper towels to drain excess oil.
Arrange the crispy taquitos on a serving platter, garnish with fresh cilantro, and serve with sour cream and salsa on the side for dipping.