China is indeed quite difficult with your own vehicle, but you can travel around China using public transport to get your fix, and then go up to Mongolia by train, for the full overland experience. Or there is a ferry between Japan, South Korea and Vladivostok.

Overland from the Pacific coast, you can start in Vladivostok and go all the way to Murmansk, cross into Kirkenes and you're basically a day's slow drive from Nordkapp, then make your way down as much of the Norwegian coast as you care.

Is your new job in Norway? Note that Norway is VERY strict about long-term residents with foreign-plated vehicles - there is a locally famous case of a business owner who used an Estonian-plated van for her Norwegian business, and the tax authorities went after her, ended up bankrupting her company. So if you're staying, anything you bring in will likely need to be put on Norwegian plates, with Norwegian taxes, which can be multiples of the car's market value.

Even shipping your car to the Asian coast will be expensive (let's assume you are shipping to Japan/Korea and taking the DBS ferry). But in theory you could buy something like a Land Cruiser in Japan, take it over on the ferry, drive it to Europe, essentially sell it for parts. Paperwork would be a bit complicated.

All that said, the others are right - this is an uncommon direction, and a lot of that is because there's not much support for it. You could come to Europe, buy a bike locally (several countries, including my own, don't require you to be a resident), and spend a very happy three months riding around this continent. Hell, a month in Norway alone is easy to fill up if you're going all the way up the coast.