Skikjøring is Norwegian for "ski driving," as in being pulled on cross-country skis, specifically by a horse, vehicle, or dog(s). In the øld days, this was a method of travel during snowy winters, but now, it's just a competitive sport. Skijoring was featured as a demonstration sport at the 1928 Olympics in St. Moritz, Switzerland.
Bandy is basically field hockey on ice instead of on a field, and also it is like soccer because there are 11 players and the field is roughly the same size as a soccer field. But you can't touch the ball with your head. You are wearing a helmet anyway, like in regular hockey. Bandy was a demonstration sport at the 1952 Olympics in Oslo, and - this is adorable - only 3 teams played: Norway, Finland, and Sweden.
Synchronized skating is exactly what it sounds like: awesome. It is also kind of like the Ice Capades and halftime shows at hockey games (I assume? I grew up in the South), but much nicer because these ladies are the crème of the crème. Watch out for accidental swastikas!Though synchronized skating - also called precision skating - has been listed as a demonstration sport on this site of questionable accuracy, no other source indicates it will be featured in the 2014 Sochi Games.
The point of speed skiing is to ski down a hill in a straight line as fast as possible. The world record holder in the sport (Simone Origone, above) clocked in at 156 mph, which is faster than a skydiver falls. For comparison, the fastest speed skater is usually moving at slower than 40 mph. Yawn. Speed skiing was last featured in the Olympics (as a demonstration sport) during the 1992 Games in Albertville, France.