You could take a bus from Oslo, ie. "Konkurrenten" has a route from Oslo Bust terminal to Kragerø which costs 300 NOK (500 for trip/return trip). The trip takes 3 hours and 20 mins.
Unfortunately, the timetable only supports dates until the 13th of June atm., but you could check here closer to your departure ( use translate.google.com) http://konkurrenten.no/route.aspx
You could also check Sørlandsekspressen ( http://www.sorlandsekspressen.no/?lang=en_GB ) and select "Oslo Bussterminal" for your "From" location. My browser isn't working all to well atm so I can't check it myself.
To get to the bus terminal, you could either use the airport express train (www.flytoget.no) which takes 20mins and is very convenient although not particularly cheap, take the local train (www.nsb.no) which uses a bit more time but is cheaper or take a bus.
For more information about Kragerø, check with http://en.visitkragero.no/
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