I go for /ˈi:strəʤən/ , which is what the LPD and the ALD give; they also give /ˈe:strəʤən/ as an alternative.
I am surprised at the Cambridge version. I have never heard it pronounced that way.
Now that you've said that I examined the Cambridge transcription /ˈiː.strəʊ .dʒən/ more closely and realised that 'ʊ' is put in italics, so they must've meant it's optional. Thanks for verification.I am surprised at the Cambridge version. I have never heard it pronounced that way.
I've also heard the first vowel as /e/ (like other words derived from a Greek οι - like economics, ecology etc).
I'd use /ˈi:strəʤən/ too.
I agree the Cambridge 'East Trojan' sounds strange.
"oe" is pronounced variably these days. We haven't had an American contributor, but since they spell it "estrogen", that might account for the /e/ pronunication. But they still say /fi:təs/ for 'foetus' or 'fetus'.
But it's /ə'sɒfəgəs/ for '[o]esophagus'.