"Illegal alien" is a term widely used to mean, approximately, "an alien who is in this country contrary to [presumably federal] law".
It appears very infrequently in the United States Code, but very commonly in state and municipal statutes, and often in discussions of immigration law.
It is not, to the best of my knowledge, defined in the United States Code.
It might seem that a definition is given by 8 U.S.C 1365(b). To introduce this passage, I first quote 8 U.S.C 1365(a) [blue emphasis mine]:
(a) Reimbursement of States
Subject to the amounts provided in advance in appropriation Acts, the Attorney General shall reimburse a State for the costs incurred by the State for the imprisonment of any
illegal alien or Cuban national who is convicted of a felony by such State.
Now for 8 U.S.C 1365(b)[blue emphasis mine]:
(b) Illegal aliens convicted of a felony
An
illegal alien referred to in subsection (a) of this section is any alien who is any alien convicted of a felony who is in the United States unlawfully and—
(1) whose most recent entry into the United States was without inspection, or
(2) whose most recent admission to the United States was as a nonimmigrant and—
(A) whose period of authorized stay as a nonimmigrant expired, or
(B) whose unlawful status was known to the Government,
before the date of the commission of the crime for which the alien is convicted.
Subclauses (1) and (2) might seem to give a general definition of "illegal alien". But note that this entire clause (b) only applies to the term as used in 8 U.S.C 1365(a). Thus it does not constitute a general definition of the term as it might be used in statutes.
Editorial note: (b)(2)B) does not make sense. If the person was most recently admitted as a non immigrant [(b)(2)], and the situation of (b)(2)(A) does not obtain [else why would (b)(2)(B) be needed] then what unlawful status is referred to in (b)(2)(B)?
Next week: The definition and significance of the term "Illegal Freemason".
Best regards,
Doug