Storch was the principal oboist for the Houston Symphony Orchestra, Carmel Bach Festival, the Bethlehem Bach Festival, Marlboro Music Festival and the Casals Festivals. Additionally, she played with the National Symphony Orchestra, the Kansas City Philharmonic, and the Puerto Rico Symphony Orchestra. She has also been professor of oboe at the Conservatory of Music of Puerto Rico, for many years at the University of Washington and guest professor at Indiana University as well as the Central Conservatory of Music in Beijing, China. She is one of the longest serving members of the Soni Ventorum Wind Quintet.
Storch has published a biography of Marcel Tabuteau, longtime Curtis Institute faculty member and world-renowned solo oboist (1915-1954) of the Philadelphia Orchestra.
- Storch, Laila (2008). Marcel Tabuteau: How Do You Expect to Play the Oboe If You Can't Peel a Mushroom?. Bloomington: Indiana University Press. ISBN 978-0-253-34949-1.
- "Curtis Alumni Award Presented to Robert Fitzpatrick (Clarinet '68) and Laila Storch (Oboe '45)". Curtis Institute of Music. Archived from the original on 11 September 2013. Retrieved 16 September 2013.
- Burgess, Geoffrey (2004). The Oboe. New Haven, Conn: Yale University Press. p. 207.