There is no reason whatever why you should be interested in Norwegian New Year’s customs, but it’s something I’ve got at hand (in the form of Sverre Østen’s book Hva Dagene Vet [What the Days Know]), published 1988 by Ernst G. Mortensens Forlag, and I haven’t got any other ideas. I translate from his account:

• The day is dedicated to Saint Sylvester, who was pope from 314—35, and bore the responsibility of leading the church from the period of persecution to the new period of peace.
• On the last day of the year people ate oatmeal and herring, as they believed their ancestors had done. The oats symbolized gold and the herring silver; which is to say, wealth.
• Many believed that empty pockets and cupboards today portended poverty, which may have been the reason many did a great deal of shopping in the last few days.
• It seems to have been particularly common to throw shoes: They would sit on a stool at the door with their backs to the living room. Grabbed their left earlobes with their right hands, and tossed a shoe with their left hand over their right shoulder. If the toe of the shoe landed pointing toward the door, they would quit and find a new job. But if the toe pointed inward, they would continue there until the next “moving day.” [It was the custom in old times for all farm workers to move to a new farm, if they chose to change jobs, on one single day of the year. I can’t remember which day it was. lw]
• New Year’s Eve is haunted, but one can scare off ghosts by strewing beans around the house during the day and saying this: “With these beans I redeem myself and mine.” The spirits will then pick up the beans and not bother the family over the coming 12 months.
• New Year’s Eve was often a dangerous evening; all kinds of witchcraft was about. To keep witchcraft away, they fired shot after shot over the house roofs. In later times it became the custom to “shoot in” the new year.

And on New Year’s Day?

• One custom was to keep the door shut to make sure the first person across the threshold in the new year was not a woman. That would be bad luck. The best thing would be a dark-haired man. He would bring good fortune.

Godt nytt år. That means happy new year.