I think you should play to your strengths and you need a "mentor" already established in the arts/ architecture field who can give you tips, steer projects your way and generally guide you in, talking you up to other professionals. Very difficult otherwise on your own to break in!
Swedes are careful, slow to make decisions and the recruiting process here takes months and months . In my experience it's very difficult to beat a Swede at their own game. Competition on the job market is very fierce even for Swedes, especially in the arts which is as you know I'm sure, already a very narrow niche and chronically underfunded in Sweden. And few jobs are full time any more.
Some background - Sweden tends to prioritise sport & technology, not the arts, both historically, politically / and in schools. All cultural funding has to come from the state, there is no tradition at all hardly of private donations. No great tradition here in my experience either of your average Joe/Sven (!) going to the theatre or art galleries ect, The urban experience is still relatively new to Swedish society. With the high tax here and low salaries, and households running on both providers working full-time, most people have very little extra cash or time to spend on the arts, unless they are really dedicated. Wealthy people leave the country and the middle classes are already stretched! So any culture/arts market in Sweden is very small. (The number of Swedes getting sports scholarships to the US for example far outweighs the number getting arts/cultural ones!). Even established arts professionals ( trained singers/ performers/artists) as well as all the established theatres in Sweden, seem to rely solely on council funding to survive . Individuals work for the state or do teaching or similar on the side, to pay the bills.
Also Sweden being such a small community, is very much about contacts , networking, where you studied, (Stockholm/Gothenburg/ Berghs, Konstfack..) people tend to work locally, not move around the country for work (unlike the US) , basically because there is no great turnover of jobs in Sweden in any field anyway- primarily because it is still comparatively difficult to fire people, plus there is no great choice of places to go geographically in any case, though perhaps if you include Copenhagen/Oslo that gives you a wider field ...
If they want a "kulturvetare" they will probably pick someone they know and trust, who is already established. In my experience you need to prove yourself first the Swedish way. If you can get one good commission or project done in Sweden, even if it means working for free or distance or whatever - then they can see on paper, "ah, this person knows what they are doing, is reliable and can actually work in the Swedish environment. " Swedes are pragmatic, they don't like chat or showiness, they like solid, factual black-and-white proof! My experience is that they don't really trust overseas qualifications - even prestigious ones - they are a bit provincial in outlook in that way, in that "homegrown is best". Despite Swedish design being so cutting-edge. Speaking bad Swedish is perceived as just unprofessional I think sadly- there is little concept of "well, she's trying"! Swedes tend to be regimental in their outlook, and have little tolerance for shoddy work or performance, or tardiness. They like efficiency!
So play to your strengths, show how you can use your languages for international contacts, impress them with your English. If they want a Swedish speaker, they won't employ a foreigner, there are already hundreds of arty Swedes out there looking for jobs.Most expats I know have started up their own business on the side, in the basement. Do something a Swede won't do. Can you open an office in Sweden representing an overseas gallery perhaps?!
Concentrate on getting to know the local art/culture scene, get your name out there. Perhaps you can start by writing articles, covering openings/galleries, profiling & showcasing Scandinavian art overseas online, in publications writing in English - show that they win by using you, you give them something no one else can do for them.
I see you are young. A huge chunk of jobs in Sweden are tied up and have been for the last 30 years, by the baby-boomers' 1940s generation, but within the next 10 years this hopefully will start to change as that generation retires. Maybe you can approach the arts courses at uni/ colleges ( Copenhagen has a long & strong tradition of art/design ect) and do a post-grad or distance course, this will give you contacts and insight, often there is a "praktikplats" which can give you a toehold into the workplace. But I have to say the artists, singers, dancers I know all combine their art with some other sort of job. Not to say it's impossible, but it's difficult.
Many Swedes spend years studying and building up a bank of experience from freelancing/ student projects. For example helping out/ volunteering at a big arts festival or similar doing admin & slog. There is a huge number of mature students in Sweden. Not unusual for arts people to not start working for money until they are nearing thirty and even though it is often temporary project work.
Final tip - the big, international corporations tend to be more open to non-Swedes, where English is the corporate language. If you work for a local town planning office, liaising with clients, planning applications, drawings - you are going to have to do that in Swedish.
Real case scenario: One (Swedish) art director I know - when he was 18 started by going round every ad agency in the area, door to door, hawking his portfolio of sketches & design ideas, offering to work for free. Got taken on as an unofficial, unpaid "trainee" by one agency, lived on bread & water for 6 months, doing work for them by helping the official team on a project and was finally offered some part-time paid project work, and eventually ended up working their fulltime after a year - but ONLY after the agency said , "you must get the proper Swedish qualifications for this job as well," which he did by studying in the evenings at the same time. Hmm...
