Nice find. At least you got the mag. Try Epps and a few others for the small parts kit. You will not need it though, if you follow some simple precautions.
These are an extremely accurate rifle, especially for an autoloader. Now the not so good news. They are a handloader's pet.
First, there is almost no ammo that will work without violent extraction and brass damage. That means rims bent, or torn off, as well as case bodies badly dented. Some rifles throw the rubber bumper off the cover. This no ammo situation includes Swedish surplus if you can find any. Apparently these were not issued to all troops in a unit. Perhaps 10% may have had one, the rest bolt actions. This would have created a logistical problem to have separate ammo and the Swedes ignored it. (At this point stop reading this and go read the section "Gas Gun Reloading in a Sierra Bullets reloading manual). Great, now if you have done that I can speed up. The Swedes never resolved the violent cycling problem. Their solutions to the problem were band-aid at best, such as oiling the rounds. Students of bolt thrust are cringing right now I know, especially with the taper of the 6.5x55 case. I'm not sure if fluted chambers were around when these were made. Too bad.
The Swedish military ammo was for use in bolt rifles of the Mauser 96 type and others where a slow burning powder was an asset. Any commercial 6.5x55 Swedish ammo you buy will also be loaded with slow burning powder, probably in the IMR 4350 range. You need to shoot reloads with faster powders, in the Reloader 15 up to Rel 12 powder range, to lower the port pressure and lessen the cycling violence. I am not advocating these powders only. Get a powder burn chart and you will see Hodgdon, Vihtavuori, IMR, Norma and others. If you can reduce this violence you probably won't need the spare parts kit.
Stick to 139-140 grain bullets.
As usual with gas gun reloading, the safe plan is to use the hardest primers available.
As for takedown, they are very easy if you keep your head screwed on. They have one of the strongest main springs of all auto loading rifles and will mess you up if you are careless. Garands and M-14s are pussycats compared to a Ljungman. Click on my name at the top left of this post. Next find the link "Find more posts by bc308". Next go to the end and find my July 2, 2006 post about takedown. Basically, never try to take it apart if the spring is compressed. When it is not compressed you are quite safe. Inverting it just lets the bolt/cover slide off easier. While you are at it check out those old posts by other CGNers. There is a wealth of info there.
As I say in the post, it was a long time ago that I had a Ljungman. In the late 60s and early 70s they were as common as SKSs are today. Every surplus dealer had them and many mainstream sporting goods stores as well. Some Swedish surplus ammo was available too, but sold without instructions and tips, such as oiling the rounds. Therefore watch the date of any post where the rifle is being disparaged. Good research and good luck.
Since that 2006 post I have acquired another. That shows you my opinion of them.