A guy came looking for his mail in my home I just moved into ?? A little nervous now?

If you do receive mail for him, simply write “RETURN TO SENDER. NOT AT THIS ADDRESS” and give it back to your postal carrier or drop it in a mailbox. If he comes by again, ask him if he registered a Change of Address with the Post Office. Second: contact your Post Office and tell them this is happening and be SURE to give them his name and CORRECT ADDRESS. You are under no obligation to do anything but do bear in mind that while a lot of mail is junk, it can also contain bills, notices, legal documents, medications, and other VERY IMPORTANT items. If you were in this guy’s situation (provided he’s telling the truth), how would you want others to treat you?

It seems some mail HAS been arriving that isn't for you or your husband.

So why are you still holding on to it? Hand it back to the mailman, or write "No longer at this address" and stick it in a mail box. Let the addressee and the Post Office sort it out between them.

You are not obliged to hand over mail to someone you don't know but you are also not allowed to hold mail that isn't meant for you.

It could be very possible that the mail was still being delivered to your home if it was his old address of where your current address is. Find out his name and just say that if you get any mail that is his, you would mail it back or just get his number and information. Although the post office should really be forwarding mail to his new residence. 

Check to see if this guy lives where he says he lives. Like knock on HIS door and assure him that you haven't received any mail for him AND will be sure to bring him any of his mail that comes to your home. If it turns out that he doesn't live where he said he lives, notify the police. This may be a scamster. Knowing what the guy looks like, knowing when he came to your home could help police ID the guy. 

Ask for his address and tell him that if you get any of his mail, either forward it on to him or take it to his address yourself.  And do just that.

If you receive any of his mail, leave it outside for him to retrieve. If he just moved recently, his mail may genuinely not be going to him and some may come to his former address/yours.

tell him you'll bring it over if you find it

Report it to the police.