Story Listening is about the story, the drawings are a tool to make it comprehensible.  Your drawings should be quick and recognizable, but they do not need to be perfect illustrations. Stick figures are fine. 

Drawings help students relax.  If students laugh, laugh with them; it will create an emotional connection, further aiding acquisition.

Quick and efficient drawing is a skill, and as with any skill, it needs practice.  Practice your drawings before the lesson as part of your prep. Google cartoon images of what you need.
Helpful tips:
Helpful books:
1000 Pictures for Teachers to Copy by Andrew Wright, Addison-Wesley Publishing Company