Heat oil in a skillet over medium heat. Add onion and garlic, stirring frequently, until softened (about 5 minutes). Transfer to the slow cooker.
Add all remaining "Add First" ingredients to the slow cooker. Stir well, ensuring the chicken thighs are in an even layer with the smooth side facing down.
Cover and cook on high for 2½–3½ hours or low for 3–5 hours, until the chicken is tender and shreds easily.
Remove the chicken and set it aside. Stir in the tortilla strips, then mix in the sour cream. Add the Cheddar cheese a handful at a time, stirring gently in between each addition until melted. Cover and let cook while you shred or dice the chicken.
Return the shredded chicken to the slow cooker. If desired, stir in lime juice and cilantro. Serve as is or over rice. Top with additional cheese, sour cream, avocado, or tortilla chips.