Argthtjtr

"My head hurts so bad, it's not even funny." Why would my head hurting be funny in the first place? It's already clearly not a joking matter. Why "guard" it from being a laughing matter, then?

I get it if it's something that may be regarded as funny at first but is actually not once we realize or find out circumstances. For example, "that old man passes gas so loud for so long, in bass, it's not even funny." It may be funny to witness, but it's not because it might be due to a medical condition.

This expression doesn't make sense. Someone please explain.

I'm so clueless about this, it's not even funny.

A Google Books search finds only two instances of "it's not even funny" in its literal (or arguably literal) sense that antedate the first appearance of the idiomatic form of the phrase.

A headline in the Columbia Alumni News, volume 14 (1922) proclaims "This Is No Joke!" with the subhead "It's Not Even Funny." And an advertisement in The Journeyman Barber, volumes 24–25 (1928–1929) [combined snippets] has this bit of doggerel:

D stands for DOLLARS

It's not even funny,

For, when you use Williams

You're sure to make money.

The next two matches, however, use the form of the expression that the OP asks about. From The Parchment (volumes 5–8) (1933[?]):

Lynn brushed the dark hair from his face with a restless movement, frowning. "I don't know. I don't even know what I want to do. I'm getting nowhere so fast it's not even funny."

And from a metrically atrocious poem called "Safety First" that appears Trans-communicator, volume 53 (1936):

You may ride the planes or take the busses,

But you don't have room to settle little fusses.

You are packed and jammed till it's not even funny,

When room and comfort by train awaits for less money.

The implication of the expression, even in the 1930s, is the one that AHuman notes in a separate answer: Our first inclination when presented with a minor inconvenience may be to make light of it and perhaps to laugh at the absurdity of the situation or at the incompetence of those responsible. But as the level of unpleasantness increases, its seriousness becomes less and less escapable through laughter, and we finally reach the point where "it's so bad that it's not even funny."

In Australian English (I can't speak for other varieties) this idiom is used for any extreme thing, not just pain or inconvenience. Often it's used without "even".
For an extremely tall tree:

That tree is so tall it's not funny

When things have extreme attributes they often become humorous. Like clowns with giant facial features. However if the extremity goes beyond a certain point then it ceases to be humorous anymore. I think this could be the origin of this idiom, but now it is just another way to express emphasis.

People like to laugh at the minor pains or struggles they have. For example, if your phone is turning off randomly every other day, you may laugh at how annoying it is and tell other people of the incident in a joking matter. Basically, it is human nature to laugh at minor annoyances. Hence, people will say things are "not even funny" to bring humor to otherwise infuriating struggles.

"My head hurts so bad, it's not even funny"

If a friend is telling you this, that is because they are really annoyed with the pain in their head and they want to make light of it. I even know at least several friends who would say this sentence laughing.

To follow up on AHuman's answer, mild annoyances are often funny. For example, if your cell phone keeps turning off (in my case, it often just doesn't beep if a text comes in, when someone answers me immediately after I've texted him), No harm comes of it, and I've adapted by checking my phone on my own when I'm expecting an answer and the phone hasn't beeped. I find it funny because there's no harm done in getting a text five minutes later, and most of the time, it's not important, even if you don't see that text for hours.

On the other hand, if this goes on for a long time, and you do miss something important--get to the hospital now, Grandma's not going to last much longer--you start to think "this phone is acting up so much lately, it isn't even funny."