If illegal alien who were charged with felony for using false ID to work need to be released ASAP, what could they use to habeas corpus them out?

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. What type of jail is he in? County? State? Federal? Is he under an ICE hold? Is there bail bond order? I strongly suggest that you or someone on his behalf contact an experienced immigration and criminal defense attorney for a face-to-face consultation and give them all of the facts surrounding his arrest. They would then be in a better position to analyze his case and advise you of his options.

Who is holding him? The jail? Prison authorities? Immigration?