Right now this situation exists in theory, but in practice pretty much nobody in the EU has any cause to try to import something via Norway, since its trade deals are quite similar to what the EU itself has.
But the EU has huge tariffs on some Chinese products, including slapping China with 30-70% tariffs on basic metal alloys in some cases[1][2].
The difference can be so large that it becomes beneficial for you as a private EU citizen to drive up to Norway yourself to fetch e.g. basic alloys at lower prices.
Nothing remotely like this situation exists within the land borders of Schengen today. There's the agreement with Iceland, but as it's an island enforcement is much easier.
1. https://www.cnbc.com/2017/06/09/reuters-america-update-2-eu-...
2. https://www.theguardian.com/business/2016/oct/07/european-un...
As for goods of mixed origin (manufactured in Norway but benefiting from Chinese inputs/components), that is indeed where things get complicated. And that's one of the reasons why trade agreements typically run many thousands of pages and take years to negotiate! But the WTO has pretty comprehensive "Rules of origin" to use as a starting point.