Note that work visas are often restricted to a specific employer (sponsor) or country, so the Norwegian work visa does not help with Latvia. Since Norway is not in the EU (but is part of the EAA and the Schengen Agreement), the easiest thing to do would be to check your curent visa status to see if you are permitted to visit as a tourist to a mainland EU country. If not, you are supposed to apply for a tourist visa from the relevant consulate office.
If you arrived in Latvia and found someone ready to sponsor you for a new work visa, you would of course be able to legally live and work here.
Check this link for the official details for non-EU nationals.
