Awesome = amazing, wonderful, extremely impressive, inspiring awe, respect and admiration etc.

• He has made an awesome achievement.
• Mary looked awesome in her dress.
• Science can show us the awesomeness of nature.
• Nehru Park is a place of awesome beauty.
• Her performance was awesome!
• The street is awesomely quiet.

Awful = very unpleasant , horrible, terrible, nasty etc.

• The backyard of his house smelled awful.
• His handwriting is awful.
• She has an awful behaviour.
• The food they served was awesome but the place they selected and the ambience were awful.
• It was an awful experience to talk to him.
• You look awful in this dress , you should go and have a change.