What is the source that tells you Anna was born in Oslo?
There is no one of the name you've listed in the 1900 or 1910 Norwegian censuses. You can search also - http://www.rhd.uit.no/indexeng.html
When she arrived in New York she had to have come by boat - did you find the passenger record of her arrival? What port did it list her coming from in Norway?
When she married she must have given information about herself to get a marriage license - what name did she give for her father? what place of birth?