Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function; add olive oil. Saute green chilies and onion in the oil, 3 to 4 minutes. Add carrots, celery, and garlic; saute for 3 to 4 minutes.
Add chicken, black beans, tomatoes, corn, enchilada sauce, chicken broth, water, potatoes, lime juice, salt, cumin, chili powder, chipotle pepper, Cajun seasoning, black pepper, and oregano. Stir well.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 14 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock and remove the lid. Remove chicken and shred meat; return shredded meat to the pot. Serve with tortilla strips on top.