His professional career began with coaching and conducting at the Zurich Stadtoper. In 1938 he left Europe for the US and settled in Los Angeles. From then on the range of his musical activities and involvements was immens, including works for radio and film studios, composing, conducting, giving solo piano concerts, and lecturing. He joined the faculty of the University of Southern California in 1945 and remained there until his death. Among his better known former students are the conductor Micheal Tilson Thomas and the composer Frederick Myrow.

In addition to teaching composition, conducting, and music history at the university, he also directed the university's symphony orchestra (1945-1958), performing much contemporary music in addition to the standard repertory. Among the American composers he included in his programs were Copland, Diamond, Foss, Ives, Piston and Ruggles. One of Dahl's most celebrated courses at the university was on Stravinsky's music, a subject of which he had intimate knowledge due to years of collaboration with the composer.

Although Dahl wrote music from an early age, his output was fairly small; his varied career provided little time for composing, and he wrote slowly and meticulously. Though his work reflected the changes in his musical environment, the individuality of his style remained strong. His early works exhibit the dissonant and densely polyphonic texture typical of German expressionism in the 1920's. The impact of America, and later, his collaboration with Stravinsky resulted in increasing clarification of texture, a trend towards diatonicism, and a pronounced interest in timbre and instrumental virtuosity. Dahl also used serial techniques in his music and evolved large, imaginatively conceived structures held together by motivic and tonal inter-relationships and complex but compelling harmonic forces.