As far as I'm aware, calling it a 'soul' in the Christian sense would be inappropriate. The term for soul was more adjacent to 'memory' and another term which is more like 'mind.' They did believe these qualities detached from the body after death and went somewhere. Though where depends on a lot of interpretation.
If you're going by the basic interpretation (end of the world/universe/etc), they're probably dead; either battling as Einherjar or as evil-dead Hel army. Which, to me, is preposterous.
In actuality? Nothing different. Ragnarök happens every year.