Sorry for the late reply.
Boy, no clue what to tell you. If you can -- I'm not sure what rules apply for other EU citizens -- I would suggest getting in on the uni. racket. Hop on some course -- whatever, really -- and try to collect whatever CSN (
http://www.csn.se/) money you might be able to get. You'll need to take a couple of credits each term, but I suspect that there's probably some English classes or whatever that you could just breeze through. Attendance is no requirement, so you could be selective with that. Might allow you to meet some people and get some random connections as well.
I used to work as a mailman with flexible hours -- basically they'd offer me shifts and I could take them or turn them down as I felt -- and that paid OK and allowed me a fair amount of flexibility in doing other things. There's a pretty big turnover of employees at most mail carriers (Posten, Bring), so they're probably almost always hiring.
I could also recommend looking into either
http://www.academicwork.se/ or
http://www.adecco.se/, both are private employment agencies that might be able to hook you up with work, the former hires students specifically. I'm not sure what requirements they place on knowing the lingo. I've had warehouse work through the latter of them, and there were people there who I don't think spoke much if any Swedish.
One thing that I would recommend you to look into is the moving/hauling business. I've used this place --
http://www.soderflytt.se/ -- a couple of times, and the owner is Yugoslav. Serbian, unfortunately, so I don't know how that translates, or if they even need people, but it might be something. On the other hand I would generally recommend Malmö over Stockholm, so idk.
I suspect that you can probably get a job in the restaurant/night-club business doing dishes or helping out in the kitchen or whatnot, but I have no real clue as to how that actually works.
Lodgings is going to be the real problem, as any sort of even remotely decent place at a reasonable price is nigh on impossible to get, at least in the big cities, given the retarded levels of command economy, rent fixing and other nincompoopery that plagues our housing market. I wouldn't know where to even start looking for a place to stay from your position, tbt, but I guess you might try to keep an eye on
http://www.blocket.se/, which is sort of a Swedish version of craigslist. People post personal ads about whatever, but unless you manage to get into some sweet commune or something it will most likely cost you a decent amount of money. Connections is really everything here, so I would suggest looking for other countrymen-in-exile to help you out.
One potential thing to do is to look for some exchange students to shack up with. They sometimes live a whole bunch holed up in a small student apartment -- against the rules, of course, but who cares -- to save on rent, and you might get some sort of a foot in through something like that. If you do enroll at the uni it might also even be possible that you could get pushed to the front of the normal student apartment line as you are a non-native. Our political class is hell-bent on running the country into the ground, so the state often tries to favor non-citizens.
There are probably smaller cities with an excess of apartments in their public housing projects, but I have no clue where. Also the labor market is obviously more limited in a smaller city.
Other than that you might try looking at couch surfing sites. There are obviously shelters, but I don't know much about how that works.
Most everything related to uni. ideas is a bit term dependent.
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Generally speaking, I wouldn't recommend it unless you're feeling adventurous.