Strictly speaking "souls on board" has a different meaning from all of your other constructions.
"There are 150 on board" can't be turned into a question. The official phraseology is "say souls on board [and fuel remaining]" -- there are no questions in ATC official phraseology. "Say number onboard" really is ambiguous and could be understood to mean only passengers.
Strictly speaking, "people" or "humans" is ambiguous too. For example is a dead person still a person? This is a rational concern with "say passengers onboard" (which might not include crew) and "say number onboard" (which is ambiguous).
But nobody with any functioning brain cells could possibly misunderstand "say persons onboard". This is an officially-acceptable civil aviation alternative to "souls onboard", as are the written abbreviations SOB and POB.
There is actually a dispute over whether "souls on board" should count entire human remains. The civil aviation standard is that a dead body is cargo and not counted. The RAF standard, and that of many other military organizations, is that dead bodies are "souls" being returned and they count them. Whether that makes sense depends on exactly what the figure is for. Is it to know how many bodies to look for? Is it to know how many people perished? (Perhaps it does not matter so long as both sides know what they're doing, and they make this a point of respect.)
In any event, no more detailed origin is known, as far as I've been able to tell. There's just lots of speculation. It was definitely originally a nautical term.
Set-piece battle
According to this Ngram, this exact wording appears to have been coined during the First World War, and usage increased dramatically during the Second World War.
The earliest use of set-piece battle I found is from 1920, in The Australian victories in France in 1918 by Sir John Monash. On page 227 is a section which begins:
And the preceding page:
Set-piece
The standalone set-piece is:
- A realistic piece of stage scenery constructed to stand by itself.
- An often brilliantly executed artistic or literary work characterized by a formal pattern.
- a. A carefully planned and executed military operation.
b. A situation, activity, or speech planned beforehand and carried out according to a prescribed pattern or formula.
It was very common in drama and when referring to fireworks displays in the 19th century. Wikipedia says:
In film production, a setpiece is a scene or sequence of scenes the execution of which requires serious logistical planning and considerable expenditure of money. The term setpiece is often used more broadly to describe any important dramatic or comedic highpoint in a film or story, particularly those that provide some kind of dramatic payoff, resolution, or transition.
And:
The term set piece or set play is used in association football and rugby to refer to a situation when the ball is returned to open play following a stoppage, particularly in a forward area of the pitch.
Military set-piece
The earliest reference I found to set-piece in a military context to describe a carefully planned and executed action (and not describing a dramatic depiction of a battle) is this 1895 footnote to Herodotus:
1905's The Times History of the War in South Africa, 1899-1902 compares carefully planned and executed operations with field-days at Aldershot Command training camp:
And:
Opposites
Monash refers to three different phases, each with very different character. From page 84 of The Australian victories in France in 1918:
Best Answer
Do a number on stage means perform a number, where number means:
The etymology of this usage of number is (Etymonline):
Imagine a program for an evening's entertainment:
If you were on Gondola Suites, you would refer to Maria as "the next number".
As the question was initially unclear as to which idiom was meant, my original answer had to do with the idiom do a number on. I kept the original, in case it's interesting:
Ngrams shows that the expression to do a number on something (meaning to act with destructive force or impact; to criticize or humiliate - OED) probably began to arise around 1970 (I turned smoothing to zero on purpose):
Here's an example:
I checked the context of the pre-1976 occurrences, and the 1900s hump is a fluke. I also don't know about that 1950 bit, but by the contexts cited, I'd say it arose in the late 1960s.
As to the evolution of the phrase, dictionaries and references are chary of suggestions, either not including the phrase, not including any etymology, or saying origin unknown. Yahoo Answers sports some brazen and insupportable speculation, as is its wont; there isn't much to see.
Here's my speculation: do a number means perform a song or dance. The Synonym Finder (1978, Google books) lists do a number on as a synonym for mock:
On would be in the sense of:
So doing a number on someone means performing an act based on someone - mocking someone.
From mocking someone the meaning morphed to humiliating someone, and then, more generally, to hurting someone and even destroying something (as in you're really doing a number on that sandwich!).