From my reading, I think the primary weapon of most members of a Viking army was the Spear. Swords, being expensive, were probably limited to the upper class. Most people would have an axe lying around the farm to take along as a secondary weapon. I'm certain Joe Collins will have more information on this topic.
Interestingly in the army lists nearly all the Vikings are classed as Blades, (with just a few Wb, Ax, Ps or Bw).
The description includes this statement: "Most warriors are classed as Blades because of the universal ownership of swords and axes and the stress placed on individual weapon skills."
However I have some Viking Bondi figures with spear so presumably there is evidence for their use, presumably with a sword or axe as a back up??
My Viking army has a mix of figures on each base. I also have different shield patterns though talking to an historical interpreter at the Royal Armouries he mentioned that bands of Vikings would have the same shield pattern.