Serly was the son of Lajos Serly, a pupil of Ferenc Liszt and a famous composer of songs and operettas in the last decades of the 19th century, who immigrated to America in 1905 with his family. Serly's first musical studies were with his father.
Spending much of his childhood in New York City, Serly played in various pit orchestras led by his father. In 1922 he returned to Hungary to attend the Franz Liszt Academy of Music in Budapest, where he studied composition with Zoltán Kodály, violin with Jenö Hubay, and orchestration with Leó Weiner.
He greatly admired and became a young apprentice of Béla Bartók. For the most part his efforts were highly praised, both by Bartók and by colleagues. Bartók's Viola Concerto took two or three years of Serly's efforts to compile from sketches into a performable piece. It is now one of the most widely performed viola pieces. One of Serly's most famous original works is Rhapsody for Viola and Orchestra. His work bringing Bartók's work to fruition has paid off in the sense that his works are often paired with those of his better known teacher, on recordings and in live performance.
Serly taught composition at the Manhattan School of Music in New York City (among other institutions) and was also a featured composer/conductor with the Danish radio orchestra. He taught orchestration to Carlyle W. Hall Sr., a trumpet player and arranger for Tommy Tucker's band, who went on to orchestrate the Broadway hit musical Man of La Mancha, as well as Cry for Us All (a musical version of Hogan's Goat), Come Summer, and several others.
American Objectivist poet Louis Zukofsky wrote a dedicatory poem to Serly, published in the avant-garde magazine, Blues, in February 1929. As a violist, Serly was chosen to be part of the NBC Symphony Orchestra for its debut season, 1937-1938, the same orchestra conducted by the legendary Arturo Toscanini. He left after the first season to concentrate on compositional activities.
In the course of rethinking the major developments in harmony found in the work of Stravinsky, Milhaud, Prokofiev, and Vaughan Williams as well as Bartók and other composers, Serly developed what he referred to as an enharmonicist musical language. In his book Modus Lacscivus (1975) he explored a set of 82 basic tertian chords. Serly titled several of his later works as being "in modus lascivus", including sonatas for violin, viola, and piano. (The 1973 edition of his piano sonata misspells the term "modus lascivus" on the cover, copyright, and title pages, putting the "s" and "c" in reverse order.) His Concertino 3 X 3 uses this compositional system, but is most memorable for its formal structure: it consists of nine movements, the first three for piano solo, the second set of three movements for orchestra without piano, and the final set combining the previous sets, played simultaneously.