Awake (to stop sleeping): awake > awoke > awoken
Awaken (to rise or be risen from sleep): awaken > awakened > awakened
Wake (to rise or be risen from sleep): wake > woke/waked > waked/woken
Waken (to rise or be risen from sleep): waken > wakened > wakened
(Past and perfect-past tenses are listed in order of frequency and preference.)
Little distinguishes these verbs from one another and few usage writers care to note distinctions beyond recommending their correct past tenses. Wake is the most common: I wake early, You will wake the baby, You will be waked at nine. It is also the sole verb that can carry the sense of remaining awake: In our waking moments. According to H.W. Fowler, awake and awaken are preferred in figurative senses—It awakens the senses, They awoke to the danger, A rude awakening—though modern usage seems to allow wake into some of these situations. Waken, a mostly literary and rarer version of wake, can usually be rewritten with the more common verb: When he wakens is less common than When he wakes. In passive structures, awaken tends to appear the most, though the other verbs may fit depending on rhythm and context: He was awakened is preferred to He was wakened (literary), He was awoken, and He was wakened. Avoid using woke in these contexts, since that word has taken a newer socio-political meaning that has nothing anymore to do with sleep.
Many writers have a tendency to follow wake with up, as in I’ll wake him up. Most phrases are, however, neater and more concise without the up, which tends to add no meaning when paired with wake (see up).