If the Julia from Finnskogen in Värmland left the parish in June 1904, here is a good possibility that she went to the closest port of emigration, which was Oslo. I found a good match for the name, date, but it just says Sweden for her place. The record is from the Norwegian Digital Archives, emigrants from Oslo.

http://digitalarkivet.uib.no/cgi-win/webcens.exe?slag=visbas...

160807 Oslo 6791 1904 Juni 30 Julia Person f u Pige 17 Sverige Minn. 14317 Sverige Prp Oscar Ii

Leaving Oslo, 1904, June 30, Julia Person, female, unmarried, Pige means single girl, or it means a girl who works for a family or farm as a hired hand, age 17, from Sweden, going to Minnesota, On the Oscar line?