A droll yarn. 'Droll' means odd or whimsical in a funny way, and 'yarn' is another word for a story. So a droll yarn is a good alternative for a funny story.
A humorous tale could be another way to say it.
A humorous anecdote. It's a short and often funny account of an event or incident.
Jokes. Jokes are short and humorous tales or statements that are meant to make people laugh, just like funny stories.
Well, 'narrative' is another word for story. It's often used to describe a sequence of events or a tale.
A synonym for 'back story' could be 'background'.
A long tale. For example, when we talk about a very detailed and extended account of something, we can use 'tale' instead of'story' and 'long tale' to mean a long story.
Headline. A headline is often used to refer to the main or top story in a newspaper, magazine, or news website.