What can we do if my boyfriend and I want to get married, I am a US citizen and he is here illegally but has his work permit?

You cannot really have him adjust status even if you get married because he entered the US unlawfully. He may be eligible for DACA but that does not make him eligible for permanent residence. He should have departed the US before he turned 18 and then he could have come back without all that time counting against him but now that he is over the age of 18, if he departs, he will be subject to the 10 year bar to reentry.

He could be able to adjust. Adjusting is the process when a person files for a green card without leaving the US. Do you know if his parents ever filed any family- base for work-based immigration paperwork on or before 4/30/2001? Please ask his parents as this is some very important information. If so, this might enable him to adjust. If you were (or are now) in the military, this could also help him, as he could get a "military parole" that should enable him to adjust. If you are not / were never in the military, and his parents never filed for anything, there is another process that involves a very short trip abroad. He can request a travel permission (an advance parole), travels, the return to the US. At the order (or airport), an officer would stamp in passport, and the he could file for an adjustment.finally, there is another process where a waiver of unlawful presence is submitted. This process is more difficult and time consuming.