Answer: Probable Strongyloides stercoralis filariform (L3) larvae.
Congratulations to everyone who wrote in with the correct answer! You all recognized that these are nematode (round worm) larvae. The clinical history and presence of larvae in the sputum are most suggestive of S. stercoralis, although it is difficult to make out specific features from these photographs to make a definitive diagnosis. The fact that they are relatively elongated suggests that they are the 3rd stage larvae (L3 or filariform) which is the typical stage that is seen in the lung during autoinfection.