Well, actually Kalmar Airport is slightly closer... would get you to be 115km from Målilla, and I belive SAS do carry flights from LHR to Kalmar Airport althoug probably a bit pricey...
Probably Oskarshamn is also closer...
All of these are "regional airports" and not all major airlines fly to these, if any. Normally it would mean that you would fly into Arlanda (Sthlm) or Bromma (Sthlm) and change to a more regional airline, e g Skyways, Kalmarflyg, Smålandsflyg etc. Independant of route chosen, I think you will be about 100km from Målilla and would need a rental to get you there.
If you want to be financially minded - perhaps fly to Nyköping (RyanAir carry cheap flights) (230km drive to Målilla - about 3hrs), get a rental and take the opportunity to get a more scenic view of Sweden!
cheers,