I once accompanied my mom on a tour of a house built around 1970 and remodeled some time in the '90s. There was no space for a refrigerator in the kitchen. None whatsoever. It turns out the previous owner wanted a huge commercial Wolf range so bad they moved the fridge into the walk-in pantry - which was beyond a breakfast nook that was on the other end of the galley kitchen - to install an 8-burner Wolf. I don’t recall whether range hood had been upgraded to match or not, I just remember thinking, “What a PITA to have to walk into the other room to get a couple of carrots!”
I saw a listing for this, tho I didn’t actually go there. Two bedroom house where you had to walk thru the bigger room to reach the smaller one. And the smaller one was painted black with lots of neon splatters - maybe applied from squirt guns? Someone did eventually buy the place. Maybe it became a one bedroom with a big walk-in closet.
In New York City, they have railroad flats, in which you have to go through rooms to get to the ones in back.
My grandparents’ house was like that - a row house built in early 1900s. But the house I cited was more of a bungalow style - a blocky little stand-alone structure.
My great-grandparents had something similar - the basement was finished but there was a small “room” under the stairs that wasn’t really , there were exposed pipes etc.
Inside that room was a toilet on top of a couple of steps , like this
As I got older, I figured out that it was because the waste pipe was too high for the toilet to be on the floor.
Ahh. The throne room. 
Hey, there’s one of those in the movie “Parasite”!
This isn’t weird for New England, but it was weird for us when we moved here: a lot of antique homes (including the one we live in) have a sequential upstairs layout, kind of like the shotgun houses described above - the stairway comes up at one end, and then it’s a room followed by more rooms. One of the ones we looked at had three in a row; ours, luckily has one room off the stairs (we put bookshelves in it) that spins off two more. But it’s listed as a bedroom, which is a bit awkward.
A sex dungeon (consensual).
Re the stand-alone potty in the basement beside the washer and dryer:
I’m old and grew up in the south. I’ve seen that sort of arrangement many times. It’s a toilet for the maid. Yes, people actually did that back in the bad old days.
A family I went to grammar school with had a swingset in the basement. Just a regular backyard one with a slide, a couple swings, monkeybars, nothing special except it was inside! And downstairs, anchored to the floor! And I still remember it.
I think I would prefer a bucket lined with a trash bag, rather than try to mount those stairs and perch in a precarious position.
I often have dreams about furiously looking for a bathroom (I assume it’s because I’m asleep but have to pee!) and often the toilets I find are scary or impractical or impossible to use (which is probably good so I don’t wet myself in my sleep) and many times they resemble that sort of ‘perched’ setup! 
The house where I spent my first 11 years had a shower built into one wall of the concrete basement. No other bathroom facilities down there, just a shower and curtain, and no other showers in the house.
I can only assume that the original owners had the shower put there so their kids could enter via the concrete mudroom, walk down the concrete stairs, and shower off without tracking mud over the rest of the house.
My grandpa’s house was like this. It was basically a shower curtain surrounding a corner of the basement, and the water drained into a floor drain. The washer and dryer stood nearby.
Like your house, you could get to the basement via the back door without having to go through any other room. After a day in the fields baling hay or cutting wheat, one could wash off the grime before going to the supper table.
Hm. I grew up in a farming community but these people weren’t farmers; the parents could have been raised on a farm, though. The split-level was built for them in 1960 but ultimately got rented out to us a couple of years later and was eventually bought outright.
Does a shed count as a “room”? Because my own house came with the fanciest shed I’ve ever seen. It’s one of those prefab TuffSheds, but then someone put in carpeting, and drywall, and a nice light fixture in the ceiling, and a skylight. I have no idea what the previous owners used it for, but it’s so nice I kind of feel bad about storing my lawnmower in there.
The one with the urinal in the shower room was built by my cousins grandfather. He was a farmer and used it to clean up after a days work. But the sink and urinal directly in the shower is what made it unique. You could not get to the urinal or sink without going under the shower.
I have seen similar setups in the Philippines where there was no separation between the toilet and the shower, where you literally could take a dump and shower at the same time
TRIGGER WARNING.
The weirdest room I ever saw in someone’s house was when I visited a friend’s house in Huntingdon, Pennsylvania, a few doors downhill from where my grandparents lived.
Personal computers were just becoming a thing.
And I saw that my friend’s mother’s PC screensaver was pornographic. It had images all over it of a woman riding a man.
That was NOT an appropriate environment for children. But I didn’t say anything because I didn’t know any better.
I think that’s called a wet room.
There are wet toilets (or whatever the term is) in some RVs, and in Amtrak bedrooms.