What are the differences among wake ,awake and waken?

There are actually four such verbs: wake, awake, waken, awaken.

The principal parts are
wake, woke or waked, woken or waked or woke
awake, awoke or awaked, awoken or awaked or awoke
waken, wakened, wakened (regular)
awaken, awakened, awakened (regular).

All four are both transitive and intransitive. In the passive the tendency is to use the regular verbs awaken or waken. Only wake takes 'up'.

They all mean the same thing.

My advice is not to use any of them if you can find another way of saying what you want to say. It's all too confusing, even for this native speaker! Emotion: smile
Students: We have free audio pronunciation exercises.
Would it be correct to say, "My granddaughter waked me up to watch television?
waked is an accepted past of wake. wake allows up. (See my previous post in this thread.)
So yes, waked me up is fine, even though woke me up is more usual where I live.

You use "awake" to describe a state of being. For example:

I remained awake till 2 in the morning.

In the above sentence, you cannot use any form of wake.
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Wake woke my waken