Set an electric pressure cooker on the saute setting and add the oil. When oil is hot, add the pork, onion, garlic, salt, chili powder, oregano and paprika. Saute until meat is browned, about 10 minutes. Turn off heat.
Add enchilada sauce, green chiles (undrained) and chicken broth, and stir to blend. Place the lid on the pressure cooker and cook using the soup setting, or cook on high pressure for 15 minutes. Release pressure using a natural pressure release.
When pressure is released, remove the lid and add the hominy. Select the saute setting and simmer the soup for 10 minutes to heat through. Add the lime juice and cilantro.