Can I sue for unlawful termination since they hired me knowing I did not qualify for the position?

It's very, very unlikely that you have any kind of a case here.  Unless you had a written contract with the company, you were an employee "at will" and that means the company had the legal right to fire you at any time for no reason at all, as long as the real reason wasn't illegal, such as racial discrimination.  I really don't see anything like that here; if the company's contract with the military requires people in your job to be citizens, they have an iron-clad legitimate business reason for letting you go.

Essentially, you were hired by mistake.  You have no right to make that mistake permanent.

Unfortunately, no. In the absence of an employment contract to the contrary, companies may generally fire people any time, for any reason, even "bad" or wrongheaded ones. In this case, however, the reason is actually valid--you did not have all the correct qualifications.

It sounds like rather than complain and seek to sue, you should be glad that you received employment for which you otherwise did not qualify.