I came across this word just very recently.

“Oxter” means that space under the arm. It does not however, mean the armpit. For example, somebody was walking up that street with a stick under her oxter.

I don’t see any clear eymology for this word. “Oxta” means “akin to” and “eax” means “axis” in pretty old version of the language. However, there is no clear derivation on why “Oxter” should mean exactly that particular space under the armpit. Also, I have very very rarely come across this word.