Hi,
Is this a single stage rubber paddle machine or a 2 stage machine?
Below applies to two stage. If it is a rubber paddle single stage, let me know and i have another thought.
Maybe this will help you. I have Murray/Craftsman that I think is the same or at least similar to your Noma (not sure). If it's totally different, then ignore this. I'm assuming that when you say auger that it is the same as the impeller belt . That's also why I'm asking the single or two stage question.
Had mine apart last year thanks to my childs rock obsession. It has the spacer , washer and nut as you mentioned, but there is also a keyway in the pulley and shaft and a key that holds the pulley from rotating on the shaft. I suspect that your problem has to do with that key or keyway damaged, allowing the pulley to rotate.
First a couple questions to clear up the impeller/auger question?
Is the impeller spinning and the augers not spinning? - then you likely have a shearpin or gearbox problem.
Is the belt pulley spinning but the impeller not spinning - then likely the keyway problem.
Note augers is the helical things that are in front of bucket. Impeller is the high speed second stage of you have a two stage.
If it is the key damaged, you'll likely need to split the machine to repair it, but may be able to at least look for a keyway on the shaft if you just loosten the nut (forget exactly how far the keyway came out on the shaft). Also check parts diagram first) If yours is the same, the shaft material is very soft steel. After removing the nut, if the pulley does not slide off easily, gently grind or file any burrs off that shaft keyway before applying any major force to the pulley to remove it. Otherwise you will bend the pulley trying to get it to come off.
Hope this helps
Ron