She traveled and lectured in different countries on behalf of the International Organisation of Good Templars (IOGT) and the Woman’s Christian Temperance Union (WCTU),[1] being proficient in English, Danish, Norwegian and German, in addition to her native Icelandic.

Her uncle was speaker of the Lower House of the National Council, and her aunt, Þorbjörg Sveinsdóttir, was prominent in public movements of every kind.

She reorganized the Women's Temperance Association, then existing in the island,[1] and when Jessie Ackermann organized the WCTU in Iceland, Olafia became President (1896).

During the period of 1895–1900, Olafia traveled through the greater part of Iceland while riding her pony, holding public meetings and working as a representative of the same temperance orders.

[1] Olafia's work as a World's WCTU White Ribbon Missionary is described in her report, which was included in the Biennial Convention and Minutes of the Executive Committee Meetings of the World's Woman's Christian Temperance Union of 1906:—[3] White Ribbon friends here wanted to have somebody to work a little among our unhappy women in the streets, and I thought that I might perhaps be able to do this, just take it quite easy, as I felt I was equal to it from day to day.

Every second and fourth Friday in the month the White Ribboners hold meetings with entertainments, Gospel reading, and refreshments, where they try to get the girls to come.

We have Baxter's "Daily Light' translated in the Icelandic; White Ribboners have distributed many copies in the hospitals in the capital city and neighbourhood.In 1899, after Ingibjörg Skaptadóttir retired from managing the monthly women's magazine Framsókn with her mother Sigríður Þorsteinsdóttir, Ingibjörg left her magazine to Ólafía and Jarþrúður Jónsdóttir.