His musical career began with the study of piano and composition. At 18 years old, he composed his first work - a concert overture. As a volunteer he participated in the Franco-Prussian War from 1870 to 1871. In 1873, Eilenberg became the music director and conductor in Stettin. In 1889, he decided to move to Berlinas a freelance composer, where his second marriage with his wife Dorothee started. They lived on 73 Bremer Street.
Eilenberg composed marches and dances for orchestra, harmony and military music, and a ballet The Rose of Shiras, op. 134. He also composed the operettas Comteß Cliquot (1909), King Midas, Marietta, and The Great Prince. The most notable music that he composed were his marches, including The Coronation March (for Alexander III of Russia), and Janitscharen-Marsch, op. 295.
Some of his music pieces, attributable to the salon and its entertainment, were The Petersburg Sleigh Ride, op. 52 and The Mill In The Black Forest, op. 57 (1885). Eilenberg completed 350 compositions throughout his life, including ten fantasies after melodies of great masters, like Ehrenkränze der Tonkunst, op. 268-277 and the suite Durch Feld und Wald, op. 119.