Nightcrawler's dad is the shapeshifting mutant Azazel who, in the comic world, has been posing as a demon since forever. At some point he claims to be known by several of Satan's aliases. The implication is that Kurt's dad is the inspiration for the Satan myth. You can argue about whether or not being immortal and acting like a demon for centureies, in fact makes you a demon...
At any rate, Nightcrawler is not officially considered a demon, but I thingk Magik could still kill him. I could see Illyana being bonkers enough, but it would take some major changes for Amanda to try to kill him.
Just about anything sharp and pointy can kill Kurt, but recently in X-Infernus, Pixie stabbed Kurt with her Soul Dagger, and pulled Magick's Soul Sword out. And yes, Azazel, Kurt's dad is the poster boy for the devil myth, though those closer to actually being the devil are those like Belasco, Mephisto, Blackheart, etc...
Take it from me he is my favorite X-Man. I have every ounce of knoledge from the Marvel Universe that involves him crammed into my head. Azazel was through ruler over a bunch of DEMON LIKE (NOT DEMON) mutants. He gave birth to many children most looked like demons and had teleportational powers. He mated with Mistique and the two had Nightcrawler. However his dad was NOT Satan and he is not a demon. And Lord Khaos is right. He is NOT demonic in nature. My goodness he is a Catholic! He nearly CONVERTED Logan completely (as he did for a short time she the old 90's X-Men the animated series episode Nightcrawler). And Nightcrawler has no magic abilities. He can only teleport. The sword would have no effect whatsoever on him.