Spoilers for the Stormlight Archive.
At the end of Words of Radiance, when the Stormfather bonds with Dalinar, he asks Dalinar to divest himself of that "monstrosity", the Blade he's currently bonded to. When he summons the Blade to do so, he can feel the screaming from the Blade in his head.
- This screaming seems to be a property of the Blades that come from the original Knights Radiant. I think it's the screaming of the dead (?) spren who forms the Blade.
- Honorblades don't cause this screaming. At least, the Honorblade that Szeth used didn't cause any screaming for Kaladin. And Honorblades aren't formed of spren, so there should be nothing to do the screaming.
- It seems that the Dalinar bonded with Talenel's Honorblade. He tells Amaram that the Blade hidden in the cavern is Talenel's, and that he bonded with that Blade because he didn't want to risk losing it.
So why is Dalinar hearing screaming? Did he bond to another Blade after the confrontation with Amaram? Is Talenel's Blade not really an Honorblade?
In chapter 16 of Oathbringer, Dalinar can hold Szeth's Honorblade without hearing any screaming, and the Stormfather confirms that Honorblades don't have minds to scream.