Heat the vegetable oil in a skillet over medium heat, and cook the turkey meat until it’s no longer pink, breaking the meat up as it cooks, 10 to 15 minutes. Pour the tomatoes into the skillet, and crush them into chunks with a spoon. Transfer the turkey meat and tomatoes into a soup pot. Stir in the hot chili beans, pinto beans, kidney beans, baked beans, and tomato paste. Bring the soup to a boil; simmer at least 10 minutes. Serve in bowls garnished with about 2 teaspoons of shredded Cheddar cheese and a dollop of sour cream.