Like fdmaxey said, these are both right. Also, if you wanted to, you could just say "I heard a noise that woke me" or "I heard a noise that woke me up" because "woke" already suggests that you were sleeping. =]

They are both correct. If you wanted to emphasize how loud the sound was, you could say: "Last night I heard a noise that woke me out of a sound sleep." This let's the listener know that it was a sizable noise and that you just weren't a light sleeper.