I only joined here so I could post here on this one thread.... I think you should to the SFI could add taking a look at the very good advice "LingoSteve" shares on his YouTube channel, where he explains how he learned Swedish through listening to audiobooks and reading. Go to YouTube and check out LingoSteve's (Steve Kaufmann) channel and look for the video "How I went about learning Swedish". (His Swedish is nearly flawless btw.) I know the method works because I've used it myself for learning Dutch and French. If that precise method is too difficult (he explains how he used thick history books...) you could instead start off by choosing something easier like "Pettson och Findus Pannkakstårtan" which you can find as a book & as a CD, and also on YouTube as a video. Easy readers might be another thing to look at, as well as the daily newspaper "8 sidor" (8 pages) by LL-förlaget publishers. You could also start to hang out and read and post on the Swedish equivalent of mumsnet, I think, which is called "Familjeliv". (You could start off by using Google Translate to help you out). Also, hang around and watch TV regularly on SVTplay (equivalent of BBC) and "Öppet arkiv" (open archive, a site with older TV shows). Find something you like, and watch it multiple times.
"How have you managed to fit in?" I must admit it's a bit difficult, and then I'm not even an expat because Swedish is my first language, I've lived here all my life, all my relatives are Swedish... All I can say is that if you're stuck with a group of people who have too many weird unwritten social rules, then you should simply move on and look for another group, because there are many sorts of people in this world and they're not all the same. I learned English as a second language, and brushed it up mainly through e-mailing with basically three penpals out of the UK; one from Blackpool, one from Wallington, and one out of Newcastle/South Shields I believe it was, I don't really quite remember. Plus nowadays I hang around and read a favourite English newspaper basically every day and sometimes listen in on "Today in Parliament" from BBC 4 just for the fun of it, and to get some listening practice.
If you're into climbing you could for example try considering joining a sportsclub like "Uppsala klätterklubb" (ukk.nu) a climbing sports club, you could be a passive member for starters. "Friluftsfrämjandet" could be another place to look, as well as "Friskis & Svettis". The choir thing that someone posted about could also be something to look at and if you're stuck at a real final outpost of civilization, maybe there's a "hembygdsförening" or similar to look into (local history society). Also check out the Red Cross for local activites, as well as the local church and even if you're not religious yourself, you could considering joining if they have some social gathering just for the practice of it, to get to talk to other people; check "uppsala stift" and navigate from there.
Good luck!