Civilrättslig is one of those terms that you find both in Norwegian and Swedish. It is a quick way of saying according to civil law. I am not aware of another, briefer, or more elegant way of putting this in English.
You will find it with all sorts legal areas in front of it, e.g. folkerettslig (international law), strafferettslig (criminal law), etc.

civilrättslig och lagfaren ägare > in private law = in personam and registered proprietor = in rem.

Quoting the same ref. as Sven P., I've included an example sentence which suggests giving more thought to the subject.

If the seller hasn't been registered yet, then s/he is a proprietor with a personal or private contractual interest only: a common occurrence in Spain.

Also the concept of 'sui juris' legal competence which the asker has raised would apply only to private individuals and not to corporations or 'statutory undertakers' like Vattenfall in the second example sentence.