Exercise the puppies, but not to the point of exhaustion. This will drain their energy and help them sleep. And yes, take them outside to eliminate at night. If you're sure that the pups don't have to go, they're fed, they've had exercise but they're still whining, you have two options: ignore it so the puppies learn it is futile, or address it so the puppies learn it is unacceptable. To address it, everytime the puppies start to whine, say "Shh!" or "No!" or "Quiet!" or what not. What will make this difficult for you will be the fact that, if it wakes you out of a sleep, you'll probably be in a bad mood. Corrections don't work unless you have an in-control and positive attitude. Never get angry or frustrated with them.. that will make them view you as weak and make it ten times worse.
Did you really get the pups at one month old?? That's crazy! If the pups were taken away at such a young age, they could have serious developemental problems. In addition, NEVER get two or more pups from the same litter! It can cause physcological damage!