The literal word-for-word translation of what you want to say is "Until when will you be living here?". Although this is grammatically correct, it sounds awkward and unnatural. Most native speakers would say this very simply with a present tense : " How long are you here for?" The answer might be "Another three weeks. I'm going home in the middle of December."

I think you can also say: Until when will you be staying here

It's wrong. Translating literally is not really the best idea. A correct way to say it is 'when when will you be staying here?' But that does not sound natural. The natural way to say it is 'how long will you be living here?'