Just some words about storytelling taken from The Story Arts website (created by storyteller & author Heather Forest)
Storytelling is a learning tool. It is a very special communicative learning tool that “encourages students to explore their unique expressiveness and increase the student's ability to communicate thoughts and feelings in a lucid manner”.
Gaining Verbal Skills
Becoming verbally proficient can contribute to a student's ability to resolve interpersonal conflict non-violently. Negotiation, discussion, and tact are peacemaking skills. Being able to lucidly express one's thoughts and feelings is important for a child's safety. Clear communication is the first step to being able to ask for help when it is needed.
Both telling a story and listening to a well-told tale encourages students to use their imaginations. Developing the imagination can empower students to consider new and inventive ideas. Developing the imagination can contribute to self-confidence and personal motivation as students envision themselves competent and able to accomplish their hopes and dreams.
Passing on Wisdom
Storytelling based on traditional folktales is a gentle way to guide young people toward constructive personal values by presenting imaginative situations in which the outcome of both wise and unwise actions and decisions can be seen.
I suggest you to explore this site about storytelling. You will find more reasons to use stories in your classes. And not only in ESL classes but also in science, maths or social studies classes.