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.
Jobs for teenagers who were attending high school in the 1920's varied depending on the region where the child lived. In the agrarian community teens helped on farms with crops and livestock. They worked in hen houses and meat plants. Many boys worked as stock boys in local stores or feed bins. In larger cities the jazz era was in full boom with Speak Easies. Teens helped package alcohol and distribute it, swept floors in taverns, eateries, and other service related establishments. Some teens worked nights in factories. Others worked for railroads as box car loaders and cleaning help. Soda shops employed teens to serve sarsaparilla. The teens of yesterday were not so different from the teens of today. The main difference was that many of them added their income to the family pot of money to help pay the bills. Today’s teen’s income are more likely to be spent on entertainment, cell phones, or transportation.