You woke him. (You did the action to him)
He awoke (from his sleep). (Only concerns the person sleeping)
Usually we use the verb "wake up" instead of "awake" and "wake". "awake and "wake" are more formal sounding verbs. Also, "wake up" can be used to say both of the cases above with the same meaning.
You woke him up.
He woke up.
Notice that the object goes between the two words of the verb when it is short. If it is a long object then it comes at the end.
Short object: I woke her up.
Long object: You woke up the large slumbering beast in the cave.