That may be regional. I hear “I’m headed out” or “I’m heading off” fairly commonly.
Just to say that headed in the sense the OP asks about is perfectly common in the UK and has been since at least the early 19th century according to OED. Not of Irish origin, it’s simply a development of earlier senses of the verb in English.
Earliest cite for box room in OED is 1927.
My hometown has three Eights in a row, but I never heard anyone recite it as “triple eight”
I’ve also lived places with paired zeros in the zip code, and never heard it given as “double zero”.
If anyone uses this method of saying a double number in the US, where is it done? I’m genuinely curious.
I should have said in my original post that box room here (Ireland) usually refers to a spare bedroom rather than a spare room in general (I’ll put that down to tiredness again if I may). It would usually have a single (twin?) bed and as several posters have rightly pointed out, a whole heap of other crap that goes in the ‘might be useful some day’ category.
A mud room would be unusual here, although my sister, who lives in jolly-hockey-sticks Surrey in the UK, does have a ‘boot room’. Dead posh.
Informative and entertaining replies, thank you.
Tayto
Heading is in very common usage. “I’m headed home” Even from a Texan: “I’m fixin’ to head out” (I am preparing to depart, good sir!)
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I use it but a) I have a box room (aka “the cats’ room,” since that’s where I keep their stuff) and b) I’m an anglophile and have run into often in my reading.
I’ve never heard the term “box room” used before. I’d just call it the spare bedroom. I’m from Pennsylvania, currently living in Arizona, with a few years spent in Denver.
As for “headed,” headed out, headed East, etc., it’s pretty common and universally understood usage. There is even a semi-famous band from Illinois called Head East.
I’d think storage closet or maybe junk room, for your box room. Unless it’s big enough to use as a bedroom, it’s not really a spare room to my mind.
Heading is fine. We use it all the time.
I’d actually not thought about ZIP codes, but most of the ones in metro Atlanta start out “300.” It’s reasonably common for people to recite theirs as “three double-oh ___ ___.”
“Mud rooms” were common in rural Upstate New York, though not in cities and towns as a rule. I haven’t heard the term used in North Carolina except by New York/other Northern state expatriates.
Not common where I’m from.
Tayto, there better not be any references to the hot press in there either. 
The zip code in the address to get tickets for The Price is Right is 90036, and when the announcer says it aloud, it’s “nine double-oh three six.”
I’ve always thought it unfairly one-sided that US publications make no effort to adapt their vernacular for overseas markets, but almost all “foreign” publications have to change terms and phrases to dumb it down for the US folks, to the point where they come to expect everything to be translated for them without any effort on their part.
I think it’s both rude to assume that Americans can’t learn new things about other countries on their own bat (in fact, it’s better if it encourages them to do so), and also far too much effort by publishers to make such changes when there’s so little gain.
Los Angeles, yes. The zip codes around downtown Los Angeles are 900xx, comonly spoken - in my experience - as 'nine double-oh one two" or similar.
That’s a “guest bedroom” over here.
Back to the matter of “cupboard.” Yes, it’s used, but I think “cabinet” is probably more common.
I say “cupboard” all the time. I hardly ever use “cabinet.” Again, I’m from the U.S. Pennsylvania-born.
I would also use “cabinets” to refer to the overall storage furnishings in the kitchen, including both cupboards and drawers.