In X-Men Origins: Wolverine, we find that Wolverine (Logan) is a long-lived Canadian who immigrated to the USA sometime between 1845 (the date of the first scene) and the US Civil War. Wolverine fights in several US wars, including the US Civil War, WW1, WW2, and Vietnam, before finally being court-martialed in Vietnam.
What is Wolverine's immigration status in the USA?
- Did he become a US citizen at some point in time?
- Does he have "grandfathered" immigration status (e.g. he is not a US citizen, but has lawful permanent residency or its equivalent due to having established residency at a time (mid-1800s) when immigration from Canada was essentially unrestricted)?
- Has he explicitly received an immigrant visa?
- Is he an illegal immigrant or otherwise out-of-status in the USA (and probably using forged paperwork)?
It makes sense that he has forged paperwork (driver's license, birth certificate, passport, etc.) anyway to hide his long life, so it makes sense that it could double to hide a lack of immigration status, but that doesn't prove anything.
I do recognize that enforcement of immigration regulations is not always universally consistent, so if Wolverine is actually out-of-status but this is explicitly ignored by US immigration enforcement officials due to his powers and/or potential, that's an answer!