Is money earned from working in an unlicensed taxi permissible?

The money you earn is not unlawful (haram), but you bear the sin of violating laws that prohibit the use of an unlicensed car, if the legal interest in that prohibition is predominant and outweighing. Otherwise, there is no sin upon you. As for what you earn through your effort and work with that car, there is no harm in benefiting from it.