awful / awfully

1a. He was awful(=very) tired.
1b. He was awfully(=very) tired.
2a. I’m awful(=extremely) sorry.
2b. I’m awfully(=extremely) sorry.
3. He sings awfully(=badly).
4a. You’re awfully(=extremely) quiet today.
4b. You’re awfully(=extremely) quiet today.
5. That’s awfully(=extremely) nice of you.
6. The pie tasted awfully(=extremely) sweet.

Please correct and comment.
Are the meanings given within brackets correct or not?
Thanks.