The fundamental description of infringement is given in USC 35 section 271(a) as:
"Except as otherwise provided in this title, whoever without authority makes, uses, offers to sell, or sells any patented invention, within the United States, or imports into the United States any patented invention during the term of the patent therefor, infringes the patent."
Note that infringement is defined as occurring within the United States. For that reason, your latter two circumstances fall outside the scope of infringement for purposes of United States law.
Under the circumstance you posit, and recognizing that the criteria for infringement as stated:
US citizens within the territory of the US may well be liable as patent infringers because they use the infringing software.
Non-US citizens are just as liable as patent infringers as users because US Courts have jurisdiction over anyone present in the US.
I think this answers the question as posed, but see USC 35 section 271 "Infringement of patent" for more details and nuance.
The text of USC 35 section 271 is available online from
the Legal Information Institute
at "35 USC § 271 - Infringement of patent"
from the USPTO
in Manual of Patent Examining Procedure Eight Edition, Revision 9 (August 2012) [MPEP]
at "35 U.S.C. 271 Infringement of Patent"
and from the Office of the Law Revision Counsel
in United States Code
at "35 USC 271: Infringement of patent". (Note that MPEP is a specific version and in the future will not be the latest. The USC from the Office of the Law Revision Counsel is a beta website, with "beta" in the URL. I expect that link to go stale in the future.)
Finally, what you did not ask is whether you are liable as an infringer. If it is determined that you "sell" your software "within the United States," you are. Further, the International Trade Commission has jurisdiction to prevent importation of infringing devices (including software devices). So, while the ITC may not be able to haul you into a courthouse in Washington, D.C., it can issue an injunction that prohibits the importation of your software. Were that to happen, anyone who defied the injunction by, say, directly downloading your software into the US from a foreign website, would be in much deeper doo-doo than a mere infringer.