Entered implies in. "How did you get into my room" and "how did you go into my room" do not show a direction and need the preposition. As they can get out/go out. Entered on the other hand always conveys someone going into something, just like how exit/leave conveys someone going out. It sounds irregular to me to say "entered into" unless you were being specific and stressing location. Say for example "Constable, the thief entered into the front room diner and not the bedroom."