I noticed that nobody mentioned that you might have overactive letdown. http://www.llli.org/FAQ/oversupply.html (talks about oversupply and overactive letdown) I do, and it's a hard thing to find info about! My DS1 used to nurse one side only, 4 minutes, every 4 hours. And he was growing just fine. DS2 (13 months) nurses both sides, probably 3-4 minutes each and I don't really keep track of how often... we demand feed.
Now, if your milk is coming out that fast, it could be that he gets tummy upset during the night that he doesn't get during the day since he'd be upright more often after daytime feeds. I'd look at maybe propping him up at night or making sure you get a good burp before laying him down. My little guy does get refluxy at night sometimes (the milk comes out so fast sometimes that he kind of has to gulp it) so I usually prop him up just a bit.
I would guess that he might be waking because his tummy hurts, but now you've conditioned him to eat every time he wakes. (I did that with DS1.) You probably will have to un-train him from that. I used "Good Night, Sleep Tight" by Kim West and Joanne Kenen. We also had my DH get up with DS1 for a few nights. When he wasn't really hungry he settled pretty quickly since he knew Daddy wasn't going to be producing any milk... and when he cried or fussed for a little while, I'd nurse him. It only took about 3 nights to reduce the number of night wakings. Babies habituate to new sleep habits pretty quickly.
There are other options, of course. I co-sleep with my DS2 so I don't have to really wake up to feed him. He tends toward the thin side, so it's not hurting anything right now to have him eating 'round the clock... and it's much less exhausting for the rest of us!
Best of luck in whatever solutions you choose for your family. :)