I am a Norse who went to Iceland with a couple of mates two years ago. We stayed in Reykjavik a few days.
I tried to find out whether there where any working girls, but couldn't find any. Reykjavik is but an average Norwegian town, and has hardly the size to attract professionals.
In Nordic culture, prostitution is frowned upon, even among hotel personnel and taxi drivers, so don't bother.
We went to a few bars one night, and just like home, you have to play the free market, competing with local blokes and US soldiers. Most of the girls in their twenties I spoke to also spoke Scandinavian (which is a relief to us Scandinavians) but their English is also almost fluent, so no problems there.
As all over the Nordic region, foreigners/foreign speakers (I switched to my flawless British English with luck) are looked upon as a bit excotic and interesting, and you'll have a conversation going in no time.
Ask them whether there are other good clubs around, and tag along if they are going to some other place (can you show me the way?), and you're even closer to a sexual encounter.
Pay for beers/drinks, but don't overdo it, as the Nordics are a bit induvidualists, and supports equality between the sexes highly. If you want to get them drunk, and buy all their drinks, say something like 'I'm here on business, and my company is paying'. That should do the trick, and they'll happily help you empty the bar.
When the nightlife comes to an end, suggest an afterparty (nachspiel) at your hotel room. If she comes with you, you'll be in heaven soon enough. If she brings a few friends, make sure that you have something more to serve in your room than the minibar can provide for. You'll still be home free, though. But don't make any business appointments the next morning, 'cause you'll still be pissed as a sailor and would hardly get some sleep before 9am.
Enjoy Iceland!
PS. Most of this applies all over the Nordic (Iceland, Faeroe Islands, Norway, Shetland, Sweden, Finland and Denmark).