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.
In live hare coursing, a bye means to pass to the next round due to a missing opponent, but not before the dog has made a lone run so it doesn't have a rest and an unfair advantage over the others.
The National Coursing Club's glossary says:
Sometimes runners are withdrawn from their courses, either because of absence, injury or weariness. Their opponent still has to run a course – a “bye” – so that it will have run the same number of courses as the next opponent. The dog may run alone or accompanied.
So in the first example above, greyhound Bismarck's opponent had pulled out, meaning he could progress to the next race, but not before having to run a punishing run to "even the playing field".
And in the second example, the day ends with greyhound Duffer running a bye on its own.
And again in the third example, where it's clear the opponent was injured the day before.
We can see bye used a lot in any of these books, and "run [...] bye" in many other coursing books. As can be seen, "get a bye" isn't in itself any kind of special set phrase (at least in these examples), but just some words used together.
Best Answer
Wikipedia
The phrase forty winks, meaning a short nap, can be traced back to Dr. Kitchiner's 1821 self-help guide, The Art of Invigorating and Prolonging Life. The phrase is mentioned in a November 1821 issue of the British Literary Chronicle, in a review of Kitchiner's book:
Here is a clip from an 1822 copy of Kitchiner's book:
The use of quotes around a forty winks nap seems to indicate Kitchiner might have borrowed the phrase from elsewhere, but I can't find it in any form earlier than his use of it. Also, Kitchiner carefully footnotes other phrases and passages from different authors throughout his book.