My second daughter was like this. I just didn't allow her to sleep more than 3 hours at a stretch during the day. I know it is hard to wake a sleeping baby when you, yourself are so tired, but if she was going to give me 4 hours of sleep I wanted it from midnight to 4am! :) Just wake him every 3 hours during the day to eat and try to keep him awake for a little while after he eats. Play with him, change his diaper, whatever. Even 15 mins. will make a difference at this age.
At night, try to feed him quickly and quietly. Only change his diaper if it is poopy. Wet can wait til morning. Keep it as dark and quiet as possible for night feedings, so he stays relaxed and will fall back to sleep quickly.
He should be sleeping longer stretches at night and shorter during the day in just a few days if you stick with it.