You normally use "He looks awful", in the sense that "looks" meas appears or seems. It makes most sense to treat it as a stative verb, and not use present continuous. Think of this as a statement of fact.

"He's looking awful" suggests something out-of-the-ordinary with Bill. Perhaps something has gone terribly wrong in his life, but it might change later. Remember that continuous form is often used for temporary situations.

In some cases the meaning is close enough so you could use either one.

Yeah @Sara I forgot the 'is'. Thans for reminding 

And thanks everyone