My goal is to build a pedal-powered hang-glider capable of traveling at least 80 kilometers per hour. Is such a unit possible in principle, or do we need orders of magnitude more power?
A hang glider that weighs, say, 275 lbs, with an L/D of 12, needs 23 lbs of thrust for level flight, or roughly, 4 HP. If you want to be able to climb with a decent rate, you need more than double that, say 10 HP minimum.
A human can make just over 1 HP in a short burst, and maybe a .1 HP sustained for a minute, even less for extended periods.
So yeah, you're off by a couple orders of magnitude. It's only possible by having massively large wings, made from exotic materials to keep the massive wings light enough. For a regular hang glider, even a high end one, foggedaboudit.
80kph in level flight? No, not with current technology. Current record holder is the Musculair II with 44.26kph. See Human Powered Aircraft.