The itinerary you have cited is not an uncommon one for me, and I do this sort of thing often. It takes a lot of legwork to put these together, and sometimes a bunch of open-jaws is how it ends up, but occasionally by choosing the right layover city, you save a bunch in time and expense.
Kayak.com is an excellent resource for these types of trips. You can input multi-city itineraries, and then compare separate tickets. In Kayak can also filter your long haul flights by layover city to find out which layovers would be most common, then later create searches based on that multi-city route.
If this were me, the first thing I would try to find is the cheapest London-Seoul-Japan(Osaka or Tokyo, whichever is cheapest) flight. Korean Airlines would be a good guess, as their hub is in Seoul. So then you just have one round trip ticket with a stopover in Seoul.
Note: once in Japan, you can get between Osaka and Tokyo by air or rail (more on that below)
The Poland part: Since Warsaw isn't that far from London (compared to Japan anyhow), you may find it cheaper to come back to London from Tokyo and book a separate flight again to Warsaw, assuming you have the time. The separate round trip tickets will likely save you much more than trying to put together a complex set of stop overs.
For your Japan destination, you can apply for a foreigner JR rail-pass that will allow you to use the Shinkansen (bullet train), and that will allow you get between Osaka and Tokyo at any times that might be convenient. Note that this type of rail-pass does not allow for the fastest train, but by taking the second-fastest and using your pass, will save you a lot over the regular bullet train fare. ( http://www.japan-guide.com/e/e2361.html ) -- in any case, domestic flights between Osaka and Tokyo are relatively inexpensive and can be purchased on short notice.
Presumably for your Warsaw to/from Gdansk, you can simply buy local flight/train tickets instead of trying to merge those in.
Cautions: Be very careful with tight connections when booking separate tickets. Carriers are not understanding at all if one flight is late and you miss a connecting flight that you booked separately. Also be aware that trying to book a single multi-city itinerary will also cause problems for the entire itinerary if anything changes in your schedule along the way.