I'd try some serious diet changes... sounds like he isn't sleeping because of tummy pain, poor guy! (and poor mommy!). Cow's milk is a HUGE cause of colic, though usually in younger babies. If he's breastfed, try cutting out all dairy in your diet (milk, cheese, butter, anything cooked with butter, etc). Also try to cut out all soy products because the soy and dairy intolerance often go hand-in-hand. If he's on formula you could try either goat's milk or a lactose-free formula. And obviously any foods he's eating make sure they are dairy and soy free and aren't gassy vegetables.
In the meantime, get somebody to take him for a night so you can get at least one night of good sleeping in. I had a severe bought of postpartum depression when my little one was waking up every hour all night long for months and months and months. You NEED sleep to be a good mommy.
Also, I usually believe that it's important for kids to have motionless sleep. But at this point you're so deep into this that you need to do whatever it takes to get the baby some rest, even if that means driving around in the car three times a day to get him into a good nap routine.
Good luck - hang in there!
OK, I just saw your updated information in the "so what happened" area. In light of that info, I'd say either co-sleep (if you aren't already) or do sleep training. We did CIO with both of our kids. The first one took right to it - three nights of crying. Second kid (who was up literally every hour all night every night from around 3 months old until six months old) took about three weeks to really "get it". But now he sleeps through the night for 12 hours each night. And he's a totally different kid depending on whether or not he gets his naps and full night of sleep. Commit to getting his naps and early bedtime (6:30 or 7) EVERY DAY for three or four weeks. Let him cry it out and I think you'll find some positive results. I know it's hard to do, but in the long run he'll actually cry a lot less because he won't be waking up crying all the time.