I cannot help with the Java application, but as you said the configuration can be done online, and the Java application is only used as a verification tool. You may find other examples, in other languages as well, on the Twitter's developers site.
Coming to the Arduino application, the main issue is that here
twitter.set_client_id(PSTR("******CONSUMER KEY*********"),PSTR("****CONSUMER SECRET*********"));
twitter.set_account_id(PSTR("***ACCESS TOKEN*************"),PSTR("********TOKEN SECRECT*************")); // first form
twitter.set_account_id(256, 384); // second, alternative form
set_account() is called twice. But you should use either the first form, with your access token and token secret passed as arguments, or the second, if these credentials are already stored in the EEPROM of the Arduino. I believe you should use the first, so you may just delete the last line and try again. If things don't work, however, you'll need an independent way to confirm that you are passing the right parameters, and this is why you should get a working Java application.