The Green Banshee is another word for Mountain Dew, a highly destructive sodie-pop. The reason for this name is the fact that Mountain Dew is green, along with the fact that it keeps you awake for hours on end, just as a screaming Banshee would.
Greg: How was your weekend?
Ben: I spent it with The Green Banshee. I was up for 97 hours straight!
Greg: But...but the weekend lasts only 55 hours.