In France the usual pronunciation of oi is /a/ as in [ʁwa], [vwa], [mwa]. The difference between /ɑ/ and /a/ is highly lost in contemporary French. What you can hear on Wiktionary is [vwa]. On the French side they only give the [vwa] IPA transcription.

Hearing [vwɑ] in an opera would probably not disturb me, I might not even notice it. I don’t know much about lyric diction but I presume you need to obtain the correct number of syllables, so pronouncing oi as two distinct syllables such as [vu.a] or [ʁu.a] would not surprise me either.

As a side note I want to point out that in Québec they still pronounce the letters oi /wɛ/ as we used to do in France a few centuries ago.

The rules for ‘traditional pronunciations’ were set down before the /a/ ~ /ɑ/ merger of modern Parisian French (around the 1930s). Hence the /wa/ ~ /wɑ/ merger is a consequence of that, and many modern books on lyric diction maintain the distinction but add that it is only found in “traditional” pronunciations.

In respected dictionaries, such as TLFi, the options are presented, and I would take these as the major authority for lyric diction. The late 20th century work The Sounds of French gives some rationale, but even then it is a bit random (basically, usually -roi will be /rwɑ/ and -as will be /ɑ/, except those that are not, such as verb forms and bras /bra/, and words ending in -roire /rwar(ə)/). Further rules such as suffixation will also cause /ɑ/ to change into /a/, e.g. sable with /ɑ/ to sablonneux with /a/.

One 1912 primer for French diction gives for the oi combination just six words with /wɑ/: bois, mois, noix, trois, pois and poids.

There is a limited amount of unanimity nowadays as to which belongs where, and I dare say that colouring the vowel while singing (for vocal quality and for intonation especially at the top of the range) would be more important [much like in Italian lyric diction].

So in essence, aller chercher dans le dictionnaire !

The other answers already offer a wealth of information, but I wanted to provide some musical perspective. I’m not a singer by training, so the best that I can offer here is observations as a listener. In all of the songs and arias that come to mind, “oi” is pronounced with /a/ (or something that approximates it), not /ɑ/:

• “À cette voix”: Roberto Alagna (slightly ambiguous pronunciation to my ears though), Leopold Simoneau

• “C’est la mois des amants bénis”: Véronique Gens, Bruno Laplante

• “L’amour est un oiseau rebelle”: Elīna Garanča, Clémentine Margaine

• “Sois calme, mon fils”: Camille Maurane

• “Quand ta voix céleste prélude au silence des belles nuits”: Pierre Bernac, Pierre Boutet, Nicolai Gedda

To the best of my knowledge, pronunciation in classical singing conforms relatively well to spoken pronunciation. There are IPA guides for some songs on websites such as SongHelix or Art Song Central. Music schools will also publish lists of resources such as this one, but you’ll have to be careful. Not all resources may teach you accurate pronunciation. (I actually linked to one of them once as an example of common anglophone errors in French pronunciation.)