How many automatic fire weapons are legally owned in the US?
As far as post-WWII guns go....
Assault rifles:
About 20,000 M-16s (many with parts kits to convert them to a 9mm submachine gun, providing their owner with two guns in one).
About 4,000 FN-FNCs.
Submachine guns:
About 25,000 MAC-10 variants (20,000 of them MAC-11/9MMs).
About 6,000 Uzi variants. 4,050 of them Group Industries Uzis (that are very nice because the legally-irreplaceable parts are deliberately made of very high grade tempered steel). 3318 of those becoming Vector Uzis after Group Industries went bankrupt (which are nicer yet because they were completed with parts taken from actual Israel-built Uzis).
General purpose machine guns:
About 1,000 M-60s.
H&K:
About 12,000 H&K guns.
Of these, about 7,200 are sears that can be freely swapped between a HK21 general purpose machine gun, HK33 assault rifle, MP5 submachine gun, and MP5K machine pistol, giving the owner an entire spectrum of weapon types with a single legally-registered sear, provided they own one of each type to drop the sear into. Most people who own such a sear do collect a range of weapon types to swap between.
I don't have a breakdown for the rest of the H&K guns, but I assume that most are probably MP5 submachine guns.