Preheat the grill to medium-high heat.
Cut the fish into 1-inch strips and season with salt and pepper. Sprinkle with lime juice.
With a rag or paper towel, grease the grill with oil to prevent sticking. Place fish on grill gently; and cook for 3 minutes on each side, turning carefully with tongs.
On the cooler outer edges of the grill place the tortillas to warm them. Transfer the warmed tortillas to a plate or a wide shallow bowl lined with a clean kitchen towel. Fold the edges of the towel over tortillas to keep them warm.
To assemble, divide the fish among tortillas and top with salsa verde and avocado slices. Squeeze lime juice over the avocado and roll up the tortillas.
Remove papery husks from tomatillos and rinse well. Cut in half and place cut side down on a foil-lined baking sheet. Place under a broiler for about 5 to 7 minutes to lightly blacken the skin.
Place tomatillos, lime juice, onions, cilantro, jalapeno peppers and sugar in a food processor or blender and pulse until all ingredients are finely chopped and mixed. Season, to taste, with salt and pepper. Refrigerate until ready to use.
Serve with chips or as a salsa accompaniment to Mexican dishes.