In a slow cooker, add the oil, onions, tomato sauce, cumin, chili powder, garlic powder, black pepper, and salt. Stir to combine.
Place the chicken in the slow cooker, turning it gently to coat it well with the tomato sauce.
Cover and cook on LOW for 8 hours or on HIGH for 4 hours, or until the sauce has thickened, and the chicken is cooked.
Remove the chicken from the slow cooker and transfer it to a plate. With 2 forks or a shredder, shred the chicken.
Add the shredded chicken back to the slow cooker. Add the lime juice and stir to combine. Taste and season with more salt, if desired.
Sprinkle the chicken with the cheddar cheese. Cover and let rest for 10 minutes, until the cheese melts.
Serve hot topped with the sour cream and cilantro, if using.