This is something even Vijay would not have expected. He might not have even thought of MLAs for various cabinet roles and important ministries. The people of TN have invited this experiment upon themselves!
Vijay does not need to form a majority Govt. He can be invited by the Governor to form the Govt and take a floor test and dare the DMK and AIADMK to vote him out. They wouldn't dare do this for now. My guess is if a floor test happens one group of MLAs may absent themselves to allow the confidence vote to pass. So theoretically he can run a minority Govt as long as the others won't join each other to vote him out.