RE: axe/sword accuracy question, neither is true. During the time of the vikings most European warriors, Norse included, used spears. Swords were very much a weapon warriors aspired to have however. If you look at Norse sagas, swords are the weapon most frequently mentioned (40%), followed by spears (30%), with axes (20%) in third.

Direct evidence regarding the weapons and armor vikings used is fairly scanty. We have the sagas, some contemporary art, some written sources, and archaeological evidence. None of these are perfect, for example, since the iron used in weapons and armor is reusable a lot of weapons and armor would have been turned into other objects when damaged. A lot of this stuff just hasn't survived to be dug up.

Touching on the question of popular perceptions: to a certain extent modern day artists just make stuff up about the Norse because no one actually knows the answer, but more often because the known answers don't fit the narrative a particular story is trying to tell. If a story requires Norse vikings to be scary alien "others" depicting them as accurately as possible means depicting them as more or less indistinguishable (to modern audiences) from other Europeans. Axes, being simple "brutish" weapons, is just one handy signifier that the person wielding it is a barbarian savage.

I'm poking around now to see if I can't find where the first time vikings and axes were parried up in pop culture.

Not a historian of the Early Middle Ages specifically, but I'd like to talk a little bit about metallurgy and the ways that metal-working technology interacts with culture in determining the types of weapons (and other tools) that a culture uses in different economic and social contexts.

That's a fancy way of saying that swords were really expensive, compared to other weapons, right up into the early 1600s. A good sword requires a steel with a fairly precise level of carbon and other trace elements in the iron, as well as a clever use of heat treatments (quenching and annealing in various fluids (air, water, oil, etc) so that the blade will have the right amount of "springiness" without being too soft (and therefore easily deformed on striking, and not holding an edge or point well) or being too hard (hard steel is good for many knives, but is brittle and therefore will shatter instead of bending when subjected to excessive strain.

I can talk about the science behind this, but that probably belongs over in /r/askscience or something.

Anyway, because of limitations in ore sources and smelting technology right up into the Middle Ages, swords were quite expensive compared to many other weapons, and were therefore seen as symbols of the warrior aristocracy. Swords required more metal per weapon than axes or polearms (spears, halberds, etc), and the metal needed much more labor-intensive processing to create a useful weapon. Many of the swords that have been found in Britain and Scandanaia from the Early Middle Ages seem to have been made in Spain or Francia, or sometimes as far afield as Central Asia and the Middle East, or at least used steel from those places, since frankly the native iron industry of 9th-centuy scandinavia couldn't produce the right kinds of low-sulfur, high-carbon steels that make the best swords. Current understanding for the manufacture of viking-age swords is tha the steel would be imported as ingots or rods, and these would be forged, worked, and above all, laboriously and repeatedly heat-treated by variably repeated sequences of quenching and/or annealing.