They all mean the same thing, however, "Ought to" is (generally) the most archaic and therefore the most formal, should is in between, and had better is the least formal (and should therefore probably only be used in informal settings). Hope this helps! Cheers.

First, I agree with the Edwin's summary, however have a few of my own takes... Second, I'd like to help with the last question. The question should be, "How DO I know when to use each one." To be honest, while I know this is a common challenge for English learners, most basic questions are going to require the use of the word "DO" (just as your first 3 questions did). Third. I'd say: "I should do my homework" = Debería hacer mi tarea; "I ought to do my homework" = Probablemente debería hacer mi tarea.; "I had better do my homework" = "Debo hacer mi tarea (para insinuar: "o quizás vaya a encontrarme en problemas"). Sí al fin de cuentas son casi lo mismo que dijo Edwin, pero mucho tendría que ver con el tono y la manera que la persona va a expresarla en la conversación. Espero que ayude un poco. Que tengas un buen día.