'Woeful' also means 'lamentable, deplorable, miserable, pitiable, pathetic'. It is often used where there is a feeling of pity or regret. It's not a frequent word, and is more typical of formal written English, usually occurring before nouns like 'state' or 'condition'. 'Awful' is more general, often used to mean 'bad, terrible, horrible'. It's a more casual word, more typical of informal spoken English. Examples: The child had not eaten for several days, and was in a woeful (miserable, pitiable) state. The child had not eaten for several days, and was in an awful (very bad) state. She slumped in her chair with a woeful (sad, miserable) expression on her face. (not 'awful') 'This food is awful!' (not 'woeful')

Just expanding a little on Gary's answer, it is quite interesting to look at the root words. Woe means misery or great unhappiness and is sometimes used in the plural woes - problems or troubles. You sometimes hear it in idiomatic expressions such as "woe betide anyone who gets in her way" Meaning you will regret it/get into trouble if you get in her way. Woeful means something like very bad or something you disapprove of. Such as the expression "Woeful ignorance" Awe means feeling of wonder or respect and some fear. Awful means very bad or unpleasant. But it can also be used as an intensifier "An awful lot of something" here it is closer to the root meaning - Awe. So both awful and woeful have changed quite a it from their roots.

Woeful is so rarely used that I would have to look it up in a dictionary to find out what the difference would be. I don't think I have ever used it. My feeling is that it more used for something that is in a sad and decrepit state, but as I said, I'm not sure. The simple answer is to know that it means something similar, but never use it.