When you go to the coast of Småland and Oskarshamn, you are actually just as close from the three big cities of Malmö, Gothenburg and Stockholm.
By car or with one of the daily bus tours from several of the larger cities, you can easily get to Oskarshamn. If you choose to fly, the nearest airport is Kalmar Öland Airport, which is served by several lines. Perhaps you combine the visit to the Småland coast with a stay on Gotland and then there are ferries from Gotland to Oskarshamn. If you take the train, there are several train connections that then connect via bus to the final destination.