I actually don't live in Iceland anymore, so I'm less up-to-date on the in-demand careers as I once was. I work for an Icelandic IT company and we are almost always hiring so I'd say IT jobs are usually still in demand. Other than that, I recommend you learn some Icelandic and try reading some job placement ads like these:
job hunting in person definitely works better than remote searching. I found my job in Iceland through personal contacts, and I know several others who have. My company actually has only advertised for an open position once. All other new hires have come via personal contacts.