Off doesn't only pair with on. You may be at work, or off work, but not on work.

Another case where off is unpaired: "off-kilter".

I'm not suggesting a pairing, but I think expecting that it might be 'on' is perhaps a bit, er, off.

To me (BrE), 'gone off' is like 'has developed off-flavours', which is like off-course & on-course but also off-side & near-side.

"On-side" is definitely a thing people say.

"Off" can also mean "away", though. If you "go off", you can "come back."

Oh yes that's true - but that's antonym to a different 'off-side'!

It may be unpaired in American English but maybe not in non-American dialects of English?

Have heard people from Great Britain say things like "x is on" before with roughly the opposite meaning as how we use "y is off".

Not sure if it's only the UK but we also use "up" and "down" as synonyms in some sitations. e.g. "I'm up for going to the pub" and "I'm down for going to the pub" mean the same thing

This is also true in the US, although I would add that being down for something connotes a tiny bit more enthusiasm than being up for it, since "down" is also used in the context of making a commitment, e.g. "put me down for two boxes" or "I'll mark you down as present."

The latter case is related more to 'writing something down [on paper]' than to a standard up/down usage that implies directionality.

And certainly being marked down has different connotations from being written up!

Don't forget markdown and markup!

I don’t have much direct experience with British English but do people really say the soda tastes on to mean the soda tastes fine?

No we don't say that. We would only say that it tastes off. We really only use the opposite with regards to events, this event is on, Daniell's birthday surprise is on, etc.

Right, the usage is the same in the US. If an event is proceeding ahead as planned, it’s on.

As well as an event, a drink on tap can be ‘on’ or ‘off’, to refer to its availability.

You’re right, but if you substitute the word “spoiled” for “off”, then jt would make sense since no one says “oh this food doesn’t taste spoiled”.