He had a peripatetic youth, learning the classics in four gymnasiums. Although this was not conducive to learning the classics, it had the benefit of showing him things from several points of view and taught him the Danish language well. After participating, on the side of the Germans, in the 1848 First Schleswig War, where he was severely wounded and spent some time in Copenhagen harbor on the prison ship Dronning Maria, Strodtmann became a student at the University of Bonn where he especially became devoted to Gottfried Kinkel.

The beginning of his writing career was mostly devoted to composing poetry, but as he became older and less revolutionary, he devoted more time to translation (into German) and literary history. He wrote books about Kinkel and Heine and published the correspondence of the poet Bürger. He translated three works from the French, but mostly concentrated on Danish and English which he knew better.

In 1852, he sailed for America, and with help from his father, the not-very-practical ex-student entered the book trade in Philadelphia, buying, selling and lending, as well as publishing a literary magazine called Die Locomotive. The business was not successful and closed in 1854, after which he traveled around the country pursuing literary interests, eventually settling in New York. Weary of his various efforts to make a living, he returned to Germany in 1856, becoming a citizen of Hamburg. He covered the Franco-Prussian War for several newspapers, and in 1871, he moved to a suburb of Berlin where he lived for the rest of his life.