I wasn't sure whether to put this in Stormlight or Warbreaker so i went for cosmere.
Essentially, we see Nightblood interact and talk with not just Vasher and Szeth but also just random characters (like Old Chapps). I find it really strange that the way he can communicate is via telepathy since this is something we don't really see in the cosmere. I had a thought that maybe Nightblood's cognitive aspect communicates with another person's cognitive aspect and the two somehow translate to physical. Not sure about the mechanics of that but i'm just throwing out ideas.
The other really out there theory i had is this: we know of one other instance where the ability to read minds and communicate with people has been plot important. Ruin and Preservation. I know Nightblood has some weird stuff going on and I also have a recollection that in Mistborn Prime, Endowment shows up with Ruin and Preservation. So i was thinking maybe Ruin and Preservation did some shardic intervention when Nightblood was made (we already know Ruin has something to do with Nightblood from WOBs). And from this, Nightblood got his ability to read minds (from Preservation) and his ability to talk back (from Ruin).
So yeah, lemme know what you guys think