What kind of monologue has been used for the main character in The Old Man and the Sea: interior monologue, soliloquy, or stream of consciousness?
Hemingway uses much interior monologue for Santiago as he ventures out alone on the sea to battle the marlin and the sharks.
Santiago talks directly to the fish, as if they are brothers, in the first person singular (I), plural (we), and second person familiar (you):
Fish, I love you and respect you very much. But I will kill you dead before this day ends.
My choice was to go there and find him beyond all people. Beyond all people in the world. Now we are joined together and have been since noon. And no one to help either of us.
Hemingway uses interior monologue for practical purposes: Santiago is alone for over half the novella. It is also realistic for an old man to mutter to himself. His de facto audience is us, of course, but also Manolin and the sea and fish. Children and nature are coupled together for a reason: it's a Biblical parable. Jesus spoke thusly to his disciples and children, his preferred audiences (rather than the formal language of the Pharisees).
Hemingway writes the dialogue in English instead of Santiago's native Spanish. Hemingway uses a few Spanish words ("la mar") to achieve some realism, but--overall--we can tell that Hemingway's not translating from one language to another. Rather, he writes in plain English, as if Santiago was speaking it for the first time. Regardless of language, Santiago would not delve into verbally complex soliloquies or stream-of-consciousness because he is a fisherman. Certainly not in English.
Hemingway, as a journalist, is all about ethos (credibility) in his writing and characters. He is writing a parable, a morality tale of a fisherman, not unlike the Biblical Jonah or Jesus. As such, he writes in the language of humility and simplicity, unadorned by hubris or stylistic experimentation. Hemingway will save the soliloquies and stream-of-consciousness for the poets and modernist contemporaries like Faulkner or Woolf.