In a resealable plastic bag, combine onions, vinegar, sugar, 1/2 teaspoon oregano, and 3/4 cup water; season with salt. Seal bag and shake to mix well. Let stand at room temperature for at least 6 hours; pickled onions will keep refrigerated for up to 1 week.
In a large bowl, combine the achiote, lime and orange juices, remaining 1/2 teaspoon oregano, and garlic; add pork, and coat well. Marinate, covered, in a refrigerator for at least 8 hours or up to overnight.
Preheat oven to 350 degrees. Form a cross with the banana leaves, and lay flat in a Dutch-oven. Place pork in center of the leaves along with any remaining marinade; brush with lard. Wrap pork in banana leaves, moistening leaves with water to prevent them from burning, and cover.
Bake until pork is very tender and falling apart, about 3 hours. Using a slotted spoon, remove meat and shred with 2 forks. Return meat to pot, and stir to moisten. To serve, place meat on a tortilla, and top with pickled onions and avocados; fold to enclose. Repeat with remaining ingredients.