Despite regional differences, there are features that are very common among Nordic Knives. The blade is narrow, straight for most of its length, with the edge curving up to meet the back at the tip. The back is straight, or only slightly clipped. The blade is single edged, and usually three to five inches long. More often than not, the finger guard is absent. The sheath holds not only the blade, but much of the handle as well. If a keeper strap is used, it fits over a stud on the end of the pommel. Often the sheath wraps around the knife and is sewn up the back. It may be dangled off the belt by a thong or hinged belt loop.
The blade grind is distinctive, and important. Blades have a single long, flat bevel on both sides of the blade. The bevel runs all the way to the edge without a significant secondary bevel. The angle of the bevel corresponds to the quality of the steel and the intended use. It's exceptionally easy to sharpen without jigs or gadgets. When sharpening, the bevel is simply laid flat to the stone, and it serves as a guide. This is an excellent system when everyone is expected to keep their knife sharp. There is a lot of discussion among knife makers and serious users about blade grind. I think the Scandinavian grind is underrated by the general user. It is widely used among woodcarvers however.
Larger knives are used also, but not as commonly. A distinctive style is the "Leuko" used in the far north by the Sammi people. It's a camp knife or machete-type all-purpose tool. The Finns also use a longer version of the narrow blade, as a combination tool and weapon.
An interesting feature of the northern knives is the handle shapes. As you get into the far north, the handles become more and more suitable only for a pulling stroke. Guards are even more rare, and the handle tapers down toward the blade. It seems that as conditions worsen for keeping a grip (due to numb hands, the wearing of mittens, etc), users learn never to push on a blade.
Here's my quick take on national and regional differences.
The Southern Swedes don't usually care what a knife looks like, and they don't want to spend much money, but it has to cut really well. I've seldom seen one that wouldn't shave out of the box, literally. The blades are tempered hard (58-62 on the Rockwell scale) and they hold an edge really well. They usually come with cheap, ugly sheaths. Often the handles are pretty ugly as well. Recently plastic has been increasingly popular for both handle and sheath. It's as if they work at making them ugly so you know every kroner of your purchase price goes into the quality of the blade. Given the quality of the blade, they are a fantastic bargain. You may want to make a better sheath, and rework the handle a little for historical settings, but you're still getting more than your money's worth. Retail prices range from $8-$30.
I bought a knife from Mora (that's the name of a Swedish town) over fourty years ago. I'm now on my third sheath. It still sees regular use and holds a razor edge. It's a great knife. I believe it cost $1.98, including postage. (That was a long time ago.)
The Norwegians want their knives to look good as well as work well. They expect good wood, a sculpted shape, and an attractive quality sheath. They're expected to last a couple of generations. They come out of the box even sharper than the Swedish knives. (They shave more smoothly). They are also ground with a single bevel on each side. They cost more and they're worth it. They tend to be tempered a little tougher than the Swedish Mora style, with a Rockwell of about 58. Styles are very traditional. There are two distinct catagories; the "everyday knife", and the "Sunday knife". The Sunday knife is highly decorative but still has a working blade. Retail ranges for a typical "everyday" knife can range from $50 to $100 or so. The Sunday knife can be much, much more.
The Finnish knives split the difference. They are nicer than the Swedish knife in appearance, but not as costly as the Norwegian knives. The styles are just a bit different, but for the most part they use natural materials with an eye toward appearance. They come in leather sheaths which are of historically accurate style, but not as heavily built as the Norwegian sheaths. They are often rather delecate looking, but are actually made to withstand the heaviest use and even abuse. They may be the strongest of the Scandinavian knives. The blades seem to be tempered just a bit softer than the Norwegian knives, about 57 or 58 on the Rockwell, and they are often ground with a slight secondary bevel. This gives a fairly sharp edge that holds up well. Many of my customers consider them quite sharp. I prefer to bring them to a single bevel, which can be a chore the first time. They are excellent knives however, and come in a wide range of prices and styles.
In all three countries the northernmost population is a separate cultural group called the Sammi, or Laplanders. The Sammi have their own knife styles, and some of the Scandinavian factories also make these styles of knives. A typical northern knife will have a wide flat pommel and a handle that tapers down to the handle. The sheaths often take almost the entire handle. Locally made Saami knives often have hand forged blades and fine hand work on handles and sheaths. Bone and antler is often used in place of wood.
There is an excellent video on YouTube of the making a tradtional Finnish knife in the style of Southern Finnland.