What are special holidays in Norway and Sweden?

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This answer deals with Norway only. I don't have much direct knowledge of Swedish holidays, but there is a large overlap between the two.

In descending order I would say Christmas, Easter and May 17 (Constitution Day) are the most important ones. New Year, Pentecost, Ascension and a few other days are also observed. It's also common to get/have one week of holiday in winter and one in autumn (and three-to-five in the summer / about two months for children).

Christmas is celebrated on December 24. The are additional traditions observed in association with Advent, and to varying degrees between December 23. and New Year. Students and many workers get/take all of Boxing Week off.

Christmas and Easter are mostly celebrated secularly, though church attendance is greater during these times and there are elements of decorations etc. based directly on the Christian roots. Easter is associated with eggs, chocolate (and other sweets), oranges, going to a cabin (in the mountains and/or woods), skiing (cross-country and alpine) and crime mysteries (a quintessentially Norwegian tradition -- a lot of crime dramas air on TV and it's very common to read crime novels). (There are also special quiz shows aired every day during Christmas and Easter -- quizzes are particularly associated with Easter.)

May 17. is celebrated by dressing up in fine dress (often traditional) and is usually spent with family. Eating out and/or eating hot dogs / ice cream and singing patriotic songs are common. The festivities are usually centred on children and brass bands playing with marching through the streets. Primary schools are meeting places for families with children, where food and drink is sold and various party games are places, with speeches, songs and other music. Most people will sing and/or hear the national anthem (Ja vi elsker dette landet) on this day. There are also other staple national songs (such as Norge i rødt hvitt og blått). Norwegian flags are carried by a large proportion of the population. Most people also wear some form of it on their shirt/suit/vest/dress. Greeting one another with "Gratulerer med dagen!" ("Happy birthday!") is usual, and the cheer "Hipp, hipp, hurra!" is common.