Deadly has several meanings, among them "fatal" (a deadly disease),"relentless" (a deadly enemy),"like death" (a deadly paleness), and "boring" (a deadly speech). Deathly means "resembling death" and "utterly": "There was a deathly odor from the tomb." "I was deathly afraid of the huge guns." In general, use deathly when you mean "death-dealing" and deadly in all other senses. Both words are intensives, strongly emotional terms that should be used sparingly.
Dictionary of problem words and expressions. Harry Shaw. 1975.