kajalsen

one dark night in the middle of the day
two dead boys went out to play
back to back they faced each other
drew their swords and shot each other
don't believe me?
why yes it's true
ask the blind man he saw it too!

The comedian Steve Allen said people laugh at 2 things --

First they laugh at things that make them feel superior like someone else falling on their derriere.

Second they laugh at something unexpected, which is really making fun of yourself because you expected something all along and you got tricked.

The bottom line is you laugh because someone made a fool of someone else or made a fool of you
If you want to write something funny write something that makes someone else look stupid and therefore makes others feel superior or write something that is totally unexpected which tricks the reader who feels stupid for making false assumptions.

When people say, "I’m so tired it's not even funny" or "my head hurts so much it's not even funny", why would it even be funny in the first place?

I believe it is an expression used to described the intensity of what they are talking about. In this case, being funny is not intense so they are basically saying, "I'm tired and I'm not joking!".