/u/textandtrowel 's post about lyres is great, and they re right that some form of these simple stringed harps existed in Scandinavia. We, sadly, don't have any complete instruments surviving from Scandinavia, but there are a few finds of lyre bridges (the piece that goes between the strings and the sound board) in Viking Age Scandinavian contexts. As /u/textandtrowel says, this lack of survival is unsurprising, as the lyres that do survive from a few centuries earlier only exist because of extraordinarily lucky archaeological circumstances.

Julia Hillberg argues (in an excellent masters thesis that you should read, if you want to know more about the archaeological evidence that does survive for lyres) that these instruments had started to go out of favor among elites by the Viking Age, and were probably most popular with ordinary, lower class persons. She also suspects that bowed lyres (which are played like a fiddle, rather than being plucked or strummed) were perhaps becoming popular by the Viking Age, but the evidence isn't as good as we'd like.

There are a few other instruments that survive. Simple bone flutes (where the marrow is removed, holes drilled into the bone, and a fipple cut) were played in the early middle ages. I know of one made from a swan bone, and you can hear a reconstruction of it played on this album. In Viking Jorvik (Coppergate, York), a boxwood set of panpipes were found. Here's a photo of the pipes, along with a flute and lyre bridge also, I believe, found in the Coppergate excavations.

I've personally made reproductions of all the above. Bone flutes are easy and fun -- try to get ahold of a long deer bone, or a Turkey leg (easier to get than swan...). The boxwood pipes aren't hard to make eith a drill press, though they're not the most satisfying things to play. But lyres are my favorite, both to make and to play. They require some basic wordworking skills, but are far simpler to put together than, say, a guitar. The Yahoo group Anglo-Saxon Lyres is full of good resources (including detailed discussion of archaeological finds), and there are a few dozen photoblogs of the construction process you can find via google ('how to make anglo-saxon lyre') which will introduce you to the basics of the process so you're not confused by the more detailed discussions in the Yahoo group, or in the archaeological literature to which Julia Hillberg's thesis (above) will introduce you.

I can't think of a single example of a Viking-Age instrument from Scandinavian archaeology. Perhaps that's not terribly shocking, since most were probably made from wood, which doesn't always survive well. In earlier times, lyres occasionally were buried with the dead as grave goods, and although many of these were heavily decayed, archaeologists have been able to figure out that a few of them were, in fact, musical instruments. But I don't think lyres were ever buried in Scandinavian graves, and they're almost impossible to identify if they were buried in other contexts. For example, archaeologists finding a decayed piece of wood on the floor of a collapsed house would probably assume it was part of the roof, rather than a crushed musical instrument. So although we don't have any evidence for Viking Age instruments in Scandinavia (at least that I know of), it's important to remember that absence of evidence isn't evidence of absence.

I would suspect—and this is only an educated guess—that Viking-Age Scandinavians would have had instruments similar to the ones found in Anglo-Saxon graves. Despite the History Channel hamming it up that Ragnar Lothbrok discovered England (or something), there was actually a lot of contact across the North Sea in the centuries before the Viking Age. In particular, the burials at Sutton Hoo just north of London have a lot in common with contemporary burials from Sweden just north of Stockholm, and both were going on into the 600s, about a hundred years before the traditional beginning of the Viking Age. There was, in fact, a lyre buried at Sutton Hoo during this period, which strongly suggests that similar lyres were being used in central Sweden as well.

For web resources, I think the best one-stop shop is Paul Butler's Anglo-Saxon Lyre. Butler works at Rutgers as an administrator rather than a professor, which I think helps him bridge both academic and more general audiences very well. For something that's a bit more academically sourced, check out The Saxon Lyre.

I would caution you that although we have an idea about what these instruments looked like and how they were built, we have absolutely no idea about how they were tuned or played. In fact, all we can really say for certain is that medieval performers didn't use the modern scale (do-re-mi ...), which was only invented in the past few hundred years, and they probably didn't use modern measures and rhythms either (the 1-2-3-4, 1-2-3-4, which you can tap out to any song on the radio), since these only date to the very late middle ages and early Renaissance. I've written a bit more about premodern music and some of our better reconstructions of it here. People who are looking for 100% accuracy might find these uncertainties discouraging, but I personally find them liberating; our partial knowledge of the past encourages experiment, not obedience.

I'd also like to ping /u/alriclofgar into this conversation, who knows more about Anglo-Saxon lyres than I do, and might perhaps have something to comment.