Recently I have been interviewed and gone through a writing task for phd position in Sweden. After that, My supervisors told me that they hope to show their labs and city to me in a visit to Sweden and they like to here my research intrest in a presentation ( that is optional).They will cover travel and accomadation. I am not from the Europe and from east Asia. They already send a invitation letter to me indicating the visit and saying I am one of the top candidates for position and therefore they would like to invite me for the arrangements of position. I could not understand this. Will they offer position for me? Anyone have experience?, thanks in advance.
They want to meet you face-to-face. This is always a good sign - it means they're seriously considering your candidacy. It doesn't mean they're offering you a position, but it does mean you're one of at most a handful of candidates they have.
If you aren't busy with something else during that period, you should probably go. You get to meet them face-to-face too. You get to see the atmosphere in their department firsthand. You get to experience the city, a sense of how expensive it will be to live there, check out potential places to stay, and so on. If they're covering travel & accommodation you won't even have to pay much to go. Worst case scenario, you could treat it as a holiday in Sweden.