How does "if you must know" differ from "you may (might) know"?

"If you must know..." typically introduces a fact that the speaker is reluctant to reveal. It's a little rude, as it implies that the listener is being nosy (intrusive). E.g., "Why weren't you at work yesterday?" -- "If you must know, I was visiting a family member in the hospital."

"You may/might know" introduces a fact somewhat apologetically. My understanding of it is that it's apologizing for wasting the time of the listener if they already know the fact. I think it also implies that the speaker isn't presuming that the listener is ignorant of the fact (to prevent insulting the listener's intelligence).

The three-day Conservative Political Action Conference ended Saturday afternoon with a meaningless presidential straw poll (if you must know, libertarian gadfly Ron Paul won for the second year in a row).

The article is written in a very chatty style, and the writer has just described the culminating straw poll as essentially meaningless (which straw polls are by their very nature: Webster's defines straw poll as "an unofficial ballot conducted as a test of opinion"). In other words, it was a nonevent.

Given that context, "if you must know" is a chatty way of implying that no one would really want to know the outcome of such a poll unless he suffered from obsessive-compulsive disorder or some kind of unhealthy fascination with trivia.

It has nothing to do with the phrases "you may know" or "you might know".

Phrases of the form "if you must ... " (or indeed "if you must!" without a following verb) are a particular idiom in English.

It uses "must" in the sense of obligation, but the idiomatic part is that it is implying "you think you must do this, but I don't agree, and I'm going to provide or permit whatever you are asking, but grudgingly".

Edit: actually, it can be used even where there's no suggestion that the other person thinks that they 'must', but just that they're doing it anyway "If you must use that word, please don't do it in front of me!"

But in the case of "if you must know", since their knowing is dependent on the speaker's telling them, the implication is indeed "if (in your opinion) you have to know".