So, etymonline provides the following comment:
found in Greek borrowings into Latin, representing Greek -oi-. Words
with -oe- that came early into English from Old French or Medieval
Latin usually already had been levelled to -e- (e.g. economic, penal,
cemetery), but later borrowings directly from Latin or Greek tended to
retain it at first (oestrus, diarrhoea, amoeba) as did proper names
(Oedipus, Phoebe, Phoenix) and purely technical terms. British English
tends to be more conservative with it than American, which has done
away with it in all but a few instances.
It also occurred in some native Latin words (foedus "treaty, league,"
foetere "to stink," hence occasionally in English foetid, foederal,
which was the form in the original publications of the "Federalist"
papers). In these it represents an ancient -oi- in Old Latin (e.g. Old
Latin oino, Classical Latin unus), which apparently passed through an
-oe- form before being levelled out but was preserved into Classical Latin in certain words, especially those belonging to the realms of
law (e.g. foedus) and religion, which, along with the vocabulary of
sailors, are the most conservative branches of any language in any
time, through a need for precision, immediate comprehension,
demonstration of learning, or superstition. But in foetus it was an
unetymological spelling in Latin that was picked up in English and
formed the predominant spelling of fetus into the early 20c.
So basically the unusual /i/ pronunciation of 'oe' originates from the Greek 'oi' via Latin.
Interestingly, even within the same field of e.g. medicine, while some words seem to be in the process of changing their pronunciation (oestrogen is pronounced both ways), others are still in the /i/ phase (diarrhoea).
That said, the above is likely just a starting point for a better, more thorough answer from somebody else...