Some babies have their internal clock backwards when they're born. My daughter is three weeks old, and while not quite as out of rhythm as your son, she is definitely more awake and aware between the hours of 7 and midnight than during daylight, and she sleeps like a rock during the day. Some of this may be inherent in a baby's programming; Mommy's expected to be able to get some work done during the day, whether it's laundry and dishes or pounding corn and scraping sabretooth tiger skins. So, baby sleeps more during the day, because a loud fussy baby out in a field with predators hunting is a prime target for natural selection. I'm not sure what the statistics would have been for a baby dying due to a loud mouth as opposed to disease, starvation or exposure, but I would guess it's not insignificant.
One thing to try is to get him accustomed to light levels increasing in the morning and then decreasing at night. Babies can't see very well, but like you and me their brains react to overall light levels, and so the use of artificial light in the evenings can mess with a baby's circadian rhythm (such as it is at less than a month old), especially if you avoid using them during the day in lieu of sunlight through windows (which can result in the house being dimmer overall during the day than at night). Avoid bright interior lights after sundown; invest in some dimmer switches (unfortunately if you've "gone green" and switched to CFLs you'll find most don't dim and the ones that do don't do it well) and in some lower-lumen fixtures like a 25-40W table lamp instead of the 180W ceiling light. Gradually lower the light level as you head toward bedtime. We've found that it's helpful to leave some overhead lights on all night, but dimmed to the minimum level we can reliably see at. This allows us to see our baby and find out what's wrong, and to head for the fridge to get a bottle, while being less piercing than a nightlight that would provide the same basic level of illumination.
Another thing is that acid reflux is common in newborns; their digestive tract muscles aren't all working in concert yet, and they swallow air which bubbles back up carrying stomach acid and half-digested formula with it. So, many newborns like being propped up with their head higher than their feet. Try a crib wedge, or bring his swing or bouncy chair into the nursery and put him down in that instead. My daughter simply can't sleep flat for this reason, and these remedies help her sleep longer and fuss less at night.
It can be gas/air; babies can be fussy after a bottle, and our daughter will occasionally (not regularly but every once in a while) get a big air bubble in her tummy that takes hours to work itself back out. One of those just happened to be at 8:00 on a Sunday night, and the wife and I were up till sunrise calming her. Bottles that allow air in while feeding are good investments; my wife and I have had good success with the Playtex VentAire bottles, as well as the Dr Brown's design. Some Similac bottles and other brands have an air vent at the base of the nipple, but it often isn't one way so you have to keep it above the liquid level, and it can introduce air bubbles into the formula. Also consider a baby formula designed "for fussiness and gas", and don't suddenly change the formula you use (at least not on a work night; we think that was one cause of the worst night we've had so far).
Another thing, more ingrained, is that lying flat on one's back is a "danger" posture for babies. They're completely helpless and exposed, and so their instinct will be to call for Mommy. The solution, says Dr Karp, is to hold a baby on its side and not its back. I've tried this and it almost miraculously stops the crying about 95% of the time, but it's not a practical solution for sleeping (it's not recommended to hold your baby while you yourself sleep, and it's not recommended to put the child in their crib in any position but on their back to prevent SIDS, nor to "bolster" them with any soft cushion). Again, putting the baby in his swing or bouncy chair so his head is propped up avoids him feeling like he's on his back. Finding a way to secure yourself so you can't roll over (like in a recliner) nor drop your baby as you sleep (a Moby wrap maybe) can be an acceptable way to hold your baby while you both get some shuteye. My wife has gotten pretty used to dozing in the rocking recliner in our daughter's nursery.
Swaddling can also help calm a baby down. It may not seem that way, as many babies initially don't seem to like being wrapped up tight in a blanket, but once you finish swaddling and calm their crying the swaddling helps them feel secure even after you're no longer holding them. We have a few HALO SleepSack Swaddles, and a few SwaddleMe wraps, and both of them work really well (the SwaddleMe wraps are excellent for swaddling your little one while he's in a car carrier or other harness restraint; the HALOS are more versatile overall), but even a receiving blanket about 3 feet square can wrap baby nice and snug. Once the crying has calmed and the baby's drifting off again, you can try putting him back in his crib. If the crying starts again, try propping him up as in earlier tips, and if you're able try maintaining some point of physical contact so he knows you're nearby (this is why we love our Co-Sleeper bassinet; it straps to the side of the bed so our daughter is right beside us without any roll-over worries).
One last thing is that babies go through a phase called "PURPLE" crying. It normally starts about two weeks and continues up to 3-4 months. During this time, babies will cry more often, for longer periods, be less consolable when they cry, may look like they're in pain, and may cry more in the evenings. This is often mistaken for "colic", but is in reality just a phase every baby goes through. PURPLE crying does many things that are actually beneficial; it helps your baby's lungs develop further, it helps your baby become attached to you (or to whomever comes most reliably when they cry), and in trying to soothe the crying, you as parents will introduce many visual, auditory and tactile stimuli that will help your baby develop mentally. Your baby WILL grow out of it, so have patience; it really does get better.