Being legally able to marry and eligible to adjust legal status in the United States are different things. Sponsoring a family member who is out of status is a lengthy, difficult and expensive process. Consult an immigration attorney in your area before you start.
He doesn't need Legal immigration status to marry you but whether you he will be able to adjust his status based on your marriage depends on many factors and in some cases may not be possible at this time. Consult with an immigration attorney about the specifics of his case.
Legal disclaimer: This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Do not rely on this advice without speaking to an immigration attorney in detail about your case. This message does not create an attorney-client relationship.
I agree , you can get married without issue, but he will need to apply for a green card in order to obtain status and travel etc
Since he is "illegal" , you should hire a n attorney to see if there are any options
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