This is an interesting post at http://blog.drwile.com/what-is-the-function-of-a narwhal-tusk/ …. what is the function of a narwhal's tusk. He doesn't reach a conclusion as such but explores various mainstream ideas and then adds his own thoughts. The narwhal tusk is in fact an elongated tooth and because of that it has nerves. In this case, sensory nerves, and what they are for, is yet to be confirmed. One of the studies has shown it has multiple purposes, one of which is that the tusk can indicate whether the sea water is beginning to freeze. A sort of early warning system so the narwhal can skeedaddle back to non freezing areas. It is of course an animal of the cold north. The narwhal is also sensitive to the amount of salt in sea water and when sea water is frozen the bottom waters become more salty.
We then have a video of narwhal feeding on cod. They use their tusks it would seem to stun the cod. However, that might not be the whole story as he wonders if the tusk is actually sensing chemicals in the water to tell the narwhal where the cod are. In that interpretation the tusk would be an important sensory organ – which is negated by the fact that it is mainly male narwhal that have tusks. Some females do have tusks but they are small in comparison to the male version -which seems to mean the tusk has other, as yet to be determined, functions. Charles Darwin suggested the tuks were there to attract mates and to signal to females their reproductive strength.