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Stress in this name should fall on the second syllable, which should have a short o (/ɒ/). Kwamikagami's change to the third syllable certainly ought to be wrong, and his suggested pronunciation of his stressed e as /ɪ/ is downright mystifying. On the other hand, I do agree with Kwamikagami that the ending -eus should appear as /iəs/, rather than the /juːs/ prescribed (but surely not practised) by a recent wave of classicists. /juːs/ would generally be impossible in names like Odysseus, Perseus or Theseus, because here -eus would be absolutely unstressed (not secondarily stressed), and furthermore /juː/ in this position would palatalize, as in tonsure */ˈtonsjʊr/ → /ˈtonʃər/. So any alleged */ˈpɝːsjuːs/, for example, would inevitably have become */ˈpɝːʃəs/, whereas we know that the real pronunciation used by actual English speakers is /ˈpɝːsiəs/.
For Idomeneus, I say /aɪˈdɒmɪˌniəs/, which sounds fine, works well with English syllable structure, and recalls the normal English way of rendering the name of the opera Idomeneo (/aɪˌdɒmɪˈneɪɵʊ/). However, I can't find a direct source for the pronunciation /aɪˈdɒmɪˌniəs/ as yet, so for now I'm giving the imperfect prescription of /aɪˈdɒmɪnˌjuːs/ published in Fagles. Q·L·1968☿ 11:12, 28 April 2009 (UTC)
The stressed /ɪ/ was probably a typo.
Greek names are normally given Latin stress in English. Since both Es are short, the Latin stress would be on the antepenult, Idoméneus, like caduceus, unless this is an established exception. Pre-antepenultimate stress is unusual is classical names. A stressed o would require a /ju:s/ pronunciation for it to be the antepenult, as here, but it still would not have been the antepenult in Latin. That would only have happened if it were abbreviated from Idómenéus, but that would still have been wrong, as the last e was epsilon, not eta. If Idoméneus is the standard pronunciation, we should note that it's idiosyncratic. kwami (talk) 12:27, 28 April 2009 (UTC)
For the purposes of Latin stress, I think eu would be considered a diphthong generally. In English the unstressed eu ought to turn up as /iə/, which is bisyllabic for me but might be a diphthong for others (RP speakers for example?). Caduceus is stressed on the second syllable (the penult, to my way of thinking) because the first u is long (cādūceus), making the second syllable heavy. If, as you mention below, Idoméneus "would be expected in poetry", then perhaps I've got hold of the wrong end of the stick. (Mind you, I could imagine that Latin might have both bisyllabic eü and monosyllabic eu; after all, Latin has Menelāüs without an au diphthong. Greek ηυ should turn up in Latin as ēu, which must necessarily be bisyllabic, I think, shouldn't it?) Q·L·1968☿ 13:18, 30 April 2009 (UTC)
It does seem to be somewhat idiosyncratic. If you check out A key to the classical pronunciation of Greek, Latin, and scripture proper names p 68 on Google Books, they give your stress pattern as the preferable one and discuss how it's a bit weird. They have I-dom′e-ne-us as the 2nd pronunciation, an mention in the notes that their first alternate (Idominéus) "must be incorrect". They also mention that Idomíneus would be expected in poetry, but don't list it in the heading. So we're left with the oddity of applying Latin stress rules while keeping the Greek diphthong, then breaking up the diphthong as in Latin. kwami (talk) 12:40, 28 April 2009 (UTC)
Well done! Yes, it's at all events a very odd name. Q·L·1968☿ 13:18, 30 April 2009 (UTC)
Hey, where would you place the stress on Bitius, Hodios (I don't know whether the iotas were long), Oceax, Peiroos, and Theotes? kwami (talk) 13:09, 28 April 2009 (UTC)
Hmm, good question. I think I would stress them all on the antepenult: /ˈbɪtiəs/, /ˈhɵʊdiɵʊs/, /ˈɵʊʃiæks/, /ˈpɪrɵʊəs/, /ˈθiːətiːz/. But I'm mentally retranslating Peiroos as Pirous, and then shortening the vowel – for some reason /ˈpaɪrɵʊəs/ seems funny to me ... though perhaps I could reconcile myself to it. Why would I palatalize Oceax but not Bitius? Hard to say. Does ambisyllabicity weaken my inclination to palatalize a t, perhaps? Q·L·1968☿ 13:18, 30 April 2009 (UTC)
I think I found at least stress assignment for all but Oceax, but I'll change the vowel in Peiroos to /ˈpɪroʊəs/. (You are of course right about the vowel: short in an open antepenult. I've been reading too many botanical names.) kwami (talk) 14:05, 30 April 2009 (UTC)