You could look into Au-pairing if you don't mind working with children, doing light cleaning and cooking, receiving a modest pocket fund, and don't mind living in the same place as your "employer". I was an au-pair in Sweden and was able to take Swedish courses paid for by my host family. And I think it may be the same for Denmark and Norway, but I'm not quite sure.
This site has information about the requirements for Denmark and Sweden http://www.aupair.se and it's also the site I used, but there are tons of other au-pair sites out there.
I think I have a responsibility to point out that YMMV. I had a wonderful host family who treated me as part of the family and not as cheap baby sitter or house cleaner. They were really great and made an effort of showing me all around Sweden, paid for my transportation cost, and gave me my space on the weekends. I know of two au-pairs who had a bit of anxiety from their host family but by large majority the other au-pairs (mostly German and Filipino) had no complaints.
Lastly, you can only au-pair for a year in Sweden without the ability to extend. But in Denmark and Norway you can do it for a total of 2 years. No clue on Finland. So while you won't be able to stay indefinitely it will however at least give you some time to learn the language(s) and experience the culture firsthand. I know some of the Filipino girls I met had spent time in Norway and Denmark before coming to Sweden.