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.
The OED has its two relevant citations under this definition (10) of the verb 'milk':
Originally in the performing arts: to exploit (a scene, situation,
line, etc.) for fullest effect; to elicit a favourable or appreciative
reaction from (an audience) and contrive to prolong it as long as
possible. Also in extended use.
The two citations are from 1950:
My feeling about the story is that you have got hold of something big,
but have not yet milked it for all it is worth.
and 1971:
They milked the applause for all it was worth, then Bart held up his
hand again.
As for ‘its’ v. ‘it’s’, it has never occurred to me that it might be anything other than the second, and the two citations support that view.
(Which edition of the OED are you using, ect? I can't find the definition you quote in the online edition which I use at http://www.oed.com/.)
Best Answer
Attempting an answer à la the formidable Sven Yargs, who's an inspiration!
Under the entry gravy, Etymonline gives:
[Etymonline]
[The Phrase Finder]
Riding the Gravy Train
Pink Floyd used the phrase “riding the gravy train” in their song Have a Cigar, in regards to, ostensibly, record executives or other music industry hanger-owns urging the band to capitalize on the success of a previous hit for “easy money” and, perhaps, to the record company itself “getting a free ride.”
In the 1970’s, truck drivers had a similar expression. A gravy hauler was a truck driver who would only drive high-paying runs.
[Culinary Lore]
However, the redoubtable World Wide Words remains somewhat uncertain about the origins of the idiom.
[World Wide Words]