how to shoot action photos in a night lighted gymnasium

I am new. I use a Sony Alpha 350. I still use the auto setting. When shooting in a night lighted gymnasium I use a 50mm 2.8 lens on auto setting with flash turned off. Often times the photos are blurry, I can often get the main subject clear (usually) but everything else is blurry. Should I use the Sport setting instead of Auto? Looking for help.