"deadly" is used in informal British English to mean "very boring". It can be used on it's own but I think that people are worried that it might be confusing, so it's often collocated with the words like 'boring', 'dull' ,'quiet' to make commons used phrases that express "really, extremely boring". I'm not sure if it's used in this way in other English speaking countries. "deathly" is as described by Sunny , but it's also often used in phrases such as "deathly quiet" (a very common expression). It just means "extremely quiet" . For example, I remember that when the final Harry Potter book 'The Deathly Hallows' was published one English newspaper wrote this: "'Harry Potter and the deathly silence. There's a powerful magic at work today which renders bedrooms and sitting rooms utterly silent, save for the rasp of turning pages..." :-)

"Deathly" means something evokes death. It is sometimes used to describe things that are unpleasant. It's not that common of a word to be honest. "Deadly" is much more common and it means something is likely to cause death. In slang it can sometimes be used to mean "extreme". ex. Climbing without a rope can be deadly. I hope this answers your question.