I think the initial oath was to the camp or the country so they didn't swap sides. A person without Christian based morals cold easily change camps in the world of their own rules and not Gods (make your yes mean yes and your no mean no!)
It was to the "LORD of
hosts" (Armies) 1 Sam 17:45, Deuteronomy 20
The KJV Old Testament Hebrew Lexicon
Strong's Number: 06635
Original Word Word Origin
abc from (06633)
Transliterated Word TDNT Entry
Tsaba' TWOT - 1865a,1865b
Phonetic Spelling Parts of Speech
tsaw-baw' Noun Masculine
Definition
that which goes forth, army, war, warfare, host
army, host
host (of organised army)
host (of angels)
of sun, moon, and stars
of whole creation
war, warfare, service, go out to war
service