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"And even in our sleep pain that cannot forget,

falls drop by drop upon the heart,

and in our own despite, against our will,

comes wisdom to us by the awful grace of God."

Aeschylus (525-456 B.C.)

I love this piece of Aeschylus' poem. Could you be so kind and explain to me which would be the correct interpretation of "awful" in this context? Does it mean "bad" grace of God? "shocking & scary" grace of God? At church, I've heard they say God is an awesome God, which means respectful and fearful and the same time. So does "awful" have the same meaning as "awsome God?"

awful [encarta.msn.com]

1. extremely bad: very bad or unpleasant, an awful smell
2. causing shock or sadness: extremely shocking, saddening, or unpleasant, an awful accident

3. sick: in poor health, I feel awful this morning.
4. very great: enormous in size, amount, number, or extent ( informal )
5. awe-inspiring: so impressive as to inspire awe ( literary )

awe

mixture of wonder and dread: a feeling of amazement and respect mixed with fear that is often coupled with a feeling of personal insignificance or powerlessness
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It means "awe-inspiring", with "awe" having the meaning you cite ("mixture of wonder and dread"). As noted, it's a literary sense; I'd go so far as to say that it's effectively obsolete (though it may hang on in religious writing, which tends to preserve archaic forms).
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The word awful is made up of awe + full, just like beautiful is beauty + ful. Aweful literally means full of awe or awe inspiring. The awful grace of God is that which is full of awe.

I read this quote in an obituary and had to look up the word "awful" in the phrase "awful grace of God ". I didn't realize that word was used to mean 'shocking' as this person was young and died suddenly.