I think the best chance of finding information on the family is to look for Anna Malena Askilsdatter in the 1865 census. If you find her, then check the church records of that parish for her marriage to Per Erik Holmberg.
A possibility is the 8 year old Anna M. Askeldsdatter listed in the 1865 census for Sand parish in Rogaland.
http://digitalarkivet.no/cgi-win/WebCens.exe?slag=visbase&am...