Heat olive oil in a heavy bottomed soup pot or dutch oven over medium heat. Add onion and cook, stirring often, 4-5 minutes or until soft. Stir in garlic and cook for 30-45 seconds.
Add green chiles, chicken, salsa, chicken stock and enchilada sauce. Bring to a boil, then cover and turn heat to low. Simmer for 20-30 minutes.
Stir in cheeses until completely melted and combined.
Cut tortillas into ½ inch strips and place several strips in the bottom of each bowl. Ladle soup over the tortilla strips and serve with optional garnishes (sour cream, shredded cheese, cilantro) and a squeeze of lime.
Store leftover soup in the fridge, covered, for 4-5 days. Reheat in a soup pot on the stove.
To Freeze: Pour leftovers into a resealable plastic bag or container (Souper Cubes are great for portioning). Freeze for up to 3 months. To reheat, microwave at 50% power or heat in a saucepan over medium-low heat. The dairy may separate; add a little cream or milk as needed.