For the chicken: Heat the olive oil in a medium skillet over medium-high heat. Sear the chicken until browned well, 1 to 2 minutes per side; set aside. Add the garlic and onions to the skillet and cook briefly. Add the chile powder, cumin, salt, tomato sauce, 2/3 cup water and the seared chicken back to the skillet. Bring to a boil, reduce to a simmer and cook until the sauce has reduced by about half, 12 to 15 minutes.
For the sour cream ranch dip: Meanwhile, whisk together the sour cream, mayonnaise, milk, cilantro, dill, chile powder, garlic, hot sauce and salt in a mixing bowl until smooth. Cover and place in the refrigerator to chill until ready to serve.
Once the sauce for the chicken is reduced, remove the chicken to a cutting board with a slotted spoon. Using 2 forks, shred the chicken, then return it to the skillet and toss to coat thoroughly. Stir in the lime juice and adjust the seasoning as needed. Set aside and allow to cool slightly, 10 to 12 minutes.
For the taquitos: Fill a large Dutch oven halfway with vegetable oil and heat to 375 degrees F.
Mix the cooled chicken with the Colby jack cheese. Divide the mixture among the tortillas, then roll the tortillas tightly, securing them with a toothpick.
Add the taquitos to the hot oil in batches of 8 to 10 and fry until golden brown, 2 to 3 minutes per batch. Remove the taquitos to a paper towel-lined plate and repeat with the remaining taquitos. Remove the toothpicks and serve alongside the sour cream ranch dip.