He may or may not be married back home, but I would guess at the least he'd be promised to someone. If he told his family he's married and therefore couldn't marry the person he was promised to, it would bring great shame on his family. They probably would react badly and likely cut him off/out. I hate to sound harsh, but it sounds like he's not prepared to go through the emotional impact of this for you. Chances are he's lied about more than just you and your son - its common for people who've left Africa to go to Europe to lie about how successful their lives are so they look good to their families.
Firstly, you have to decide if how important him not telling them about you really is too you. If you can accept that his life now is here with you, that he probably tells them other lies too, that thats culturally acceptable to him and that you'll just never meet them and they won't be part of yours of your baby's lives then you can forget about it and move on. Does he go home often? If not, maybe it doesn't really matter what his life was out there.
If you can't accept it then you need to find out what the real situation is.
Snooping would be very hard if you know little about his life in the Sudan. I think it was fingerscrossed who suggested catching him off guard by asking him outright - that sounds like your most likely method of finding out. I would also suggest turning it right round and instead of getting upset about it, play up to it. If he's promising to tell them when your married, make out like your doing everything possible to get married. Say things like "it'll be great when we're married, I can't wait to meet your mum, she's going to love her grandson" See how nervous he gets. You'll be able to see if he's serious about doing it or if he's just going to put other barriers in the way. I really would try hard not to make it an argument - IME (African husband) telling him he must do something is an absolutely sure fire way to stop him from doing it! I really do have the most easy going husband in the world but once he digs his heels in, it takes a heck of a long time to change his mind. You need to play the long game on this if its really really important to you.
I'm really sorry your having to go through this, hope you find a way to work things out.
Oh and African families are generally quite extended - there will ALWAYS be someone who speaks English somewhere!