Hi,
As Stumpy says, there is already a lot of information in this forum regarding housing & costs in Iceland.
There are three categories of work visa in Iceland, all of which are generally issued for a year at a time.
Professional athlete: doesn't apply to your situation
Qualified professional: given to people who have skills hard to come by in Iceland. Lots of IT people have this one
Temporary shortage of labor: I have never heard of anyone being on this one.
You can read more about visas at http://utl.is/index.php/en/work
The type of job you describe wanting is the kind of thing that generally goes to people from other EEA member countries as it requires no visa for the employer, and paperwork is relatively simple for them. If you want to work legally in Iceland, you need a national ID number (Kennitala) which is rather a hassle to get if you're coming from the US. Even after I had a work visa from the immigration authorities, it still took weeks for my kennitala to be processed. If you don't have a visa, you're going to be out of luck trying to get a kennitala.
So my advice to you is consider whether you can volunteer or do WWOOF during a stay that's under 90 days.