It is important to remember that while many European warriors were members of a landed elite and thus of the upper classes of those societies, many of the vikings were self-owning peasants and thus middle class.

Swords were expensive back in those days. And while the vikings, especially the great men and Jarls and their hird (personal retuny) often used swords, regular people more often used axes. In a pinch, a woodworking tool axe could be used in combat, but it seems that many axes were actually dedicated weapons of war.

Apart from the Ulfberht swords (which were probably imported, but there are those that claim the vikings could have done it themselves) that have been found in many warrior graves and are made of high-quality steel, viking iron and low-grade steel was full of impurities and thus often brittle. It is easier to forge an axe-head and have it be able to sustain the wear and tear of combat and keep together than it is to make a sword.

Swords were simply more expensive, harder to make and often (if not rare Ulfberhts) prone to cracking or breaking during the strain of combat due to impurities in the iron. Thus only the upper classes of both European and viking societies had swords to a larger extent.