The family's surname prior to immigration to USA was Annanolli sometimes spelled Annanolle or Annanole but typically Annanolli. I believe it was shortened either by the immigrant family members arriving from Finland to USA or the border/customs officials. Most of the Ollis entered through Canada to Vermont and travelled onward to Michigan. Mostly likely they travelled west across New York State to Buffalo, then on to Detroit before heading north to Seney and Grand Marais, Michigan.
Within my own family of Olli ancestors dates were as follows.
Josua John Annanolli who became John Olle of East Tawas, Michigan; Grand Marais, Michigan, and Lake County, Ohio arrived alone. John was born 6 June 1869, Himanka, Lansi-Suomen Laani, Finland. He died 12 July 1951 Painesville, Lake, Ohio, USA. John immigrated in 1887 and originally settled settled in AuSable Iosco Co MI. He was married to Amanda Kaanta 20 July 1889 in Au Sable, Iosco, Michigan, USA. At some point the couple relocated to Grand Marais in Alger County where Amanda died of a heart attack 4 August 1901 having been weakened by tuberculosis. Amanda left behind eight children. The first six were born in Oscoda, Iosco County, Michigan along the shores of Lake Huron. Eldest was Limon Olli born about 1890. Second eldest was Jalmara J. aka Elmer J. Olli, born 26 May 1895, who became a champion featherweight boxer in Los Angeles, California, USA. Second eldest was Saime Olli (Haglund) born June 21, 1891 who settled with her husband in East Tawas, Michigan. Saime Olli was living with her parents at age 18 in 1910 in Grand Marais but returned to East Tawas, Iosco County to get married to Herman Haglund. Third eldest was Allie Celine Olli (Richard) born in 1893. Allie married Timothy M. Richard in Ashtabula, Ohio, USA on 1 November 1913.