Pulse onion and garlic in a food processor until finely chopped. Add juice and next 3 ingredients; pulse 2 times or until blended.
Place steaks in a large shallow dish or heavy-duty zip-top plastic bag, and pour onion mixture over steaks. Cover or seal bag, and chill 1 hour, turning occasionally.
Remove steaks from marinade, discarding marinade.
Grill, covered with grill lid, over medium-high heat (350° to 400°) 5 minutes on each side or to desired degree of doneness. Cut across grain into thin slices.
Stir together mayonnaise and salsa; spread evenly on 1 side of each bread slice. Arrange steak evenly on half of bread slices; top with avocado slices and remaining bread slices.