If you're at all easily overstimulated, I would suggest getting some foam earplugs. If the baby is really worked up and screaming, having that right in your eardrum while you're trying to soothe him/her can be incredibly stressful. Taking the edge off the scream can help you to be calmer, which will help baby calm more easily. It can mute the extremes of the screaming.

Otherwise, taking turns at night with your wife to tend to the baby will help you both sleep better. Finding something that baby likes and feels soothed by early on is a big help. For our daughter, she LOVED being tightly swaddled (MASTER THIS!) and after a few months, sucking on her thumb (we still swaddled the other arm & her legs). For my son, he loved the pacifiers - he would go to sleep with one in his mouth, one in each hand, and then we would sprinkle a few around the crib so that we could easily find one in the middle of the night if needed or, as he got older and started moving around his crib, he could easily find one.

There's no easy way around the lack of sleep issue. It sucks. (I'm doing it now, again, with a new puppy - and remembering why I didn't want to have more kids! lol...) One thing that can help when you put baby to bed is if you have a hot water bottle and can warm the sheets slightly before setting him/her down. Moving from your arms to cold sheets can be jarring and wake an exhausted baby.

Also, Vertigo is right on with the Baby Bjorn carrier - that thing was worth its weight in gold. Babies love it, and you can keep them close and cuddled while still being able to function with both hands as necessary.