I am interested for the term used when instances of two consecutive vowels sounds are in different syllables, such as:
thrOUGHOUt, abbrevIAtion, immedIAte, barrIER, cOExist, promiscUIty, crEAte, pallIAtive, amIAble etc
This is called hiatus: two consecutive vowel sounds in separate syllables; as opposed to diphthong, two consecutive vowel sounds in the same syllable. In hiatus, the vowel sounds need not be different, though it is rare for language to actually distinguish between two hiatus of the same vowel, and a long vowel: e.g., [e.e] vs. [ee]
As jlovegren mentioned, two sucessive vowels in separate syllables are said to be "in hiatus". Sometimes there is variation between pronunciations with two vowels in hiatus and pronunciations with diphthongs.
In English, many vowel phonemes have a tendency to be pronounced as "closing diphthongs": at the end of the vowel, the tongue gets "closer" to the roof of the mouth. Speaking generally, there are 7 such sounds. (Of course, you can get a different number if you use a different analysis, or if you try to account for regional splits (usually with very little contrastive load) that exist, such as the aɪ/əɪ split that exists for some North American speakers with "Canadian Raising" or the əʊ/ɔʊ split that exists for some British English speakers because of the effects of /l/ coloring a preceding vowel.)
There are three "true diphthongs" in Standard English where the tongue starts out in a very different place from where it ends up:
/aɪ/ (the vowel sound of buy; sometimes written /aj/, /ɑj/, /ai/, or in non-IPA transcription /ay/),
/aʊ/ (the vowel sound of now; sometimes written /aw/),
/ɔɪ/ (the vowel sound of boy; sometimes written /oɪ/, /oj/, or in non-IPA transcription /oy/).
There are also four vowel phonemes that are often pronounced as closing diphthongs where the tongue doesn't move as far, and the extent of diphthongization varies between accents and depending on the context. These are sometimes called "tense" vowels (the exact meaning of this term unfortunately seems to vary between authors):
/i/ (as in see; also written /iː/; sometimes written /ij/ or /ɪj/ or in non-IPA transcriptions /iy/),
/u/ (as in glue; also written /uː/; sometimes written /uw/ or /ʉw/),
/eɪ/ (as in day; sometimes written /e/, /ɛɪ/, /ei/, /ej/, /ɛj/, or in non-IPA transcriptions /ey/),
/oʊ/ (as in toe; also written as /o/ (for American English) or /əʊ/ (for British English); sometimes written as /ou/, /ow/ or /əw/).
The glide phonemes /j/ (the "y" sound in "yellow") and /w/ are articulated in a similar manner to the end of a closing diphthong, so many speakers find that in a sequence of a closing diphthong followed by another vowel, it sounds like there is a /j/ or /w/ sound in between the vowels (as mentioned in a comment by John Lawler).
As far as I know, in English, the first of two vowels in hiatus can never be /ɛ/, /æ/, /ʌ/, or /ɒ/ (the vowels of pet, cat, cut, and British English pot, respectively).
When the first vowel is stressed, I think there are at most 9 options for it:
any of the 3 "true diphthongs": /aɪ/, /aʊ/, /ɔɪ/ (as in quiet, allowance, annoyance)
any of the 4 "tense" (closing-diphthongized) high or mid vowels: /i/, /u/, /eɪ/, /oʊ/ (as in European, acuity, chaos, stoic).
in a number of accents, the first of two vowels in hiatus may be one of the 2 non-front non-closing-diphthong vowels /ɑ/, /ɔ/. However, in certain British English accents, sequences of /ɑ/ or /ɔ/ + another vowel may be separated by epenthetic /r/ in at least some contexts: for example, drawing is commonly pronounced as "droring". I'm not sure if it's common in British English to pronounce baaing as a homophone of barring. In some North American accents, such as mine, there is only one vowel phoneme corresponding to the /ɑ/, /ɔ/ of other accents.
As far as I know, the second vowel has no real restrictions based on the identity of the first, although some combinations are more or less common (and it seems likely that there are some gaps: I just doubt that the pattern of gaps can be described in any simple way). Also, when the first vowel is stressed, the second vowel is often unstressed, which means it may be subject to vowel reduction.
The phonetic process of "smoothing" may result in the use of a single vowel in place of a stressed vowel followed by an unstressed vowel in hiatus in certain contexts. The rules for this vary significantly between varieties; one example from my dialect is that I usually pronounce "Graham" as /græm/ (in broad phonetic transcription, [greə̯m]) rather than as /greɪəm/.
When the first vowel is unstressed, it's a bit harder to give a comprehensive list of all options. It could be:
one of the 2 neutralized high vowels /i~ɪ/ or /u~ʊ/ (as in median, gradual). In traditional British "Received Pronunciation", these sounds were identified with the "lax" vowel phonemes /ɪ/ and /ʊ/; however, in contemporary British English, they are often identified with the "tense" vowel phonemes /iː/ and /uː/, and in American English, it is typical for these to be transcribed as "tense" vowels. As with the stressed tense vowels, the transition between /i~ɪ/ or /u~ʊ/ and the following vowel often sounds similar to a glide phoneme (/j/ or /w/).
either of the 2 "tense" (diphthongized) mid vowels: /eɪ/, /oʊ/ (aorta, oasis); however, unstressed /eɪ/ may be reduced for some speakers in some contexts to /i~ɪ/ (see my answer to Which English words feature reduction of diphthongs like /eɪ/ to /i/?) and unstressed /oʊ/ may be merged for some speakers (not sure if in perception or production, or both) in some contexts with /əw/: Merriam-Webster transcribes heroine as ending in "-ə-wən".
a "true" diphthong: I think only /aɪ/ is at all common (in words like biography), but /aʊ/ and /ɔɪ/ seem to be possible (as in however, Loyola, Toyota). That said, it seems possible that at least some speakers think of the words that appear to have /ɔɪ/ followed by a stressed vowel as actually having a phonemic glide /j/ (corresponding to the use of the letter "y" in the spelling); it's a bit hard to say. Also, I'm not sure if the first syllable of "however" is actually unstressed; now that I think about it, it seems like it might have secondary stress.
One of the 2 non-reduced non-front non-closing-diphthongs /ɑ/, /ɔ/: These are pretty uncommon in unstressed syllables as they often reduce to /ə/ in this context. However, it seems possible that they occur unreduced for some speakers in certain loanwords or things like that (e.g. the name Raúl). There appears to be a tendency to merge /ɑ/ in an unstressed syllable followed by the high front vowel /i/ or the glide /j/ with the diphthong /aɪ/: an example is the word naive, from French naïf/naïve with hiatus (/naif/, /naiv(ə)/); English speakers may identify the vowel in the first syllable with either /aɪ/ or /ɑ/.