What was a common job in the 1920's for a teenager who still was attending high school?

You may get a different range of answers. What is fact is that, prior to the fall of the market and the Great Depression, the 1920s were prosperous post-War years and jobs were very easy to be found. Teenagers did not even need to finish High School and they were quite free to make a living on their own.

As far as what they could do, just focus on the service and consumer industry for what would have been the easiest to get: In the restaurant industry, car shops, servers, gas station attendants, theatre clerks, ushers, cooks. Anything that has to do with industry, customer service, and services to consumers would have been their first hit.