I know anything about cars.

What's the problem with the third example?

I know everything about cars.
I know all about cars.
I know anything about cars.

The third example sounds funny, perhaps because you don't hear it too often.

I would say "i know something" instead...

<I would say "i know something" instead...>

But "something" cannot express "all", where "any" can.

In that case, you would say "I know everything about cars."

<In that case, you would say "I know everything about cars.">

Or "all about cars".

The question is, why can't we use "I know anything about cars"?

Maybe because "any" is the direct object and is not followed by a sentence.

I know any person. NO (no sentence and it's the direct object)
I know any person you might think of. (sentence)
X antivirus will protect you against any virus. (it's not the direct object)

That's true when no modals are around, because I think you can say "You can know anything about cars, just read Wikipedia" or "I'll be able to know anything".

That's what I think, but I am not a native speaker of English.