Jackson is possessed and is only semi-aware of what's going on with Nidhogg, and his willpower is strong enough to exert some emotions on Nidhogg(who's less an actual manifestation of the spirit and more of a mutated and twisted version of the individual. As for Nidhogg the spirit, he can't be killed really. He's a spirit of chaos that has feasted upon the roots of the world tree and thus is connected to the world in such a way that makes complete eradication impossible. To permenantly get rid of Nidhogg, you'd have to find a way to seal the entirety of the spirit, which is harder than it sounds since he's basically a god(or possibly stronger since he's the harbinger of the world's end )