You only have to submit a report to the NTSB for an Aircraft Accident and that is the FAA definition of accident (serious injury, substantial damage, etc) and a list of selected incidents. If you hit a bird, squirrel, or whatever else and it does not qualify as an accident or one of the selected incidents, it does not have to be reported. They do have the Aviation Safety Reporting system that is voluntary but that is primarily used to save your ass after busting a FAR although I don't see why it couldn't be used to submit a birdstrike (I think this is the current voluntary reporting system the article refers to).