Probably nothing, actually. I've ordered lots of stuff from Japan before (I'm a modeler, and Japan has a lot of the best stuff), and it's never cost me anything other than what the vendor charged for shipping.
In fact, now that I think of it, I've ordered stuff from all over before: UK, Australia, Italy, Poland, China... never got any kind of customs fees or taxes. The US seems to be unusually relaxed about that stuff compared to other countries. Probably the "silver lining" of trade deals made to streamline the exporting of our manufacturing jobs, unfortunately.
As far as Olympus themselves goes, most of the website is in Japanese, but on the
terms and conditions page it sort of seems like there aren't any special exceptions for overseas shipping other than time frames, and the fact that they mention them repeatedly (and it's in English) seems to indicate they expect/want overseas orders.
Based on past experiences buying stuff from Japanese vendors, I'd expect you'll get a choice between SAL and EMS shipping. SAL means it'll go by boat, so it'll take a few weeks, but'll be cheaper (around 8-12 bucks). EMS means it'll go by plane, so it'll arrive fast, but it'll be expensive (maybe around 20 bucks). That's just guesstimation on my part though. The lack of special mention on the T&C page combined with the implied expectation of overseas orders (and the fact that the "free shipping" tags are in English) makes me think anything marked "free shipping" will in fact be free.
