This isn’t a word. This doesn’t even /sound/ like a word.
Let’s break it down.
Regardless is defined as “without paying attention to the present situation; despite the prevailing circumstances” (1). Another way to rephrase this is simply “in spite of everything”. A way you’d use this in a sentence is as follows: “Although it is likely my attempt at educating stupid people is pointless, I will continue regardless.”
Now, the prefix ir-, as a lot of other prefixes (such as in-,im-, and il-) means “not” or “the opposite of” (2). For example, if something is irrational, it is not rational. If something is irresponsible, it is not responsible. Similarly, if the term irregardless was a word, it would mean “not regardless”.
To be fair, the people who use the not-word, or ‘irword’, irregardless, usually simply mean regardless. For example, someone might say, “Irregardless of what you think, I’m going to take break dancing lessons.” In that case, your stupidity is simply the inability to understand what you’re saying. Simply correct it. But then there are people who might actually try to use the ‘irword’ irregardless to actually mean “not regardless”. In which case, props for understanding basic word structure, and I shame you for not understanding a double negative.
Ir- means not, or the opposite of. -less means without, or lack of. And for the same reason ‘irrationalless’ and ‘ircolorless’ are ‘irwords’, so is irregardless. Because, get this, irregardless simply means /regard/! The ir and the less would cancel each other out, and that would leave you with the rough phrase of ‘to regard’.
So even the grammatically correct sentence structure of irregardless would be along the lines of “Irregardless to the data provided, I find it prudent to follow our research and create ‘Jenga Hour’ at work.” But the less stupid sounding way to say that, and coincidentally the proper way to say it, would be “In regards to the data provided, I found it prudent to follow our research and create ‘Jenga Hour’ at work.”
So to summarize:
Irregardless - not a word.
(depending on situation and tier of stupidity)
(1) This is a little interesting. I decided to use the Google definition, so just search on Google “define regardless”. The reason for this is that the Dictionary and M-W definitions simply weren’t engaging. They were two or three words at best and yielded no examples. Still, if you don’t believe me, you’re welcome to look up the Dictionary and M-W definitions yourself.
(3) http://en.wikipedia.org/wiki/Jenga — I’m citing this one for anyone out there who doesn’t know what Jenga is. And to them, I say, play Jenga. It’s sort of awesome.
Author’s Note: ‘Irword’ is not a real word. I was using it ironically. Please, for the love of God, do /not/ make this a thing. Please.