PostNord a publicly owned company, but it's an ordinary company by its legal status. The latter is what matters for the legal rights of its employees. Because PostNord is in direct competition with privately owned businesses, it should operate under the same rules as its competitors. It could be seen as an unfair an possibly illegal advantage if its employees were not allowed to strike.
That is not the sense of the word "private" used by jltsiren:
>>> its employees have the same right to strike as any other private sector employees.
A business owned by the state is part of the public sector, not the private sector. This isn't a question of whether shares of its stock are traded on a public exchange. Companies with publicly-listed stock are still private companies in this sense.