Heat the oil in a frying pan over medium heat. Place the fish in the pan and cook for 2-3 minutes on each side. Use a fork to check the fish. It should be flaky and milky white when done. Overcooking will cause it to be dry and tough.
Divide the fish into 5 servings. Place one serving of fish on each tortilla. Squeeze the limes over the fish, add the avocado slices, and top with the shredded cabbage and your favorite salsa.