He was trained as a bookbinder, but went on the stage in 1903. Because he did not earn enough money for his living he was looking for alternatives. In 1909/1910 he joined Nordisk Film Company.
He worked under directors such as August Blom and Lau Lauritzen Sr. It was Lauritzen who brought him together with Harald Madsen as a comic couple.
Together with Harald Madsen, Schenstrøm formed the Danish comedian couple Fyrtårnet og Bivognen (Fy og Bi), known as "Long & Short" in England and "Ole & Axel" in the U.S.
He emigrated with his family to Chicago in the 1890s, but the family returned 3 years later to Denmark after his father was hit by a streetcar.