When does the ɔ have a "o̞" OR "ɞ" sound?

Question

Hi French linguists and French people,

I am just a beginner, so I might be wrong. I am teaching myself ONLY on Duolingo and the internet. I am really trying to learn the difference between ɔ and o̞. I find that the ɔ has a "o̞" OR "ɞ" sound ONLY before L and R and sometimes M and N, whereby the ɔ sounds like ɔ as in FOR.
[ɔ] (open O)
[o̞] (mid O)
[o] (closed O)

Here are some examples.

alors (ɔ as in for) [alo̞r],
absolument [apso̞lymɑ̃],
d'ordinaire (ɔ as in for) [do̞ʀdinɛʀ],
soleil [so̞lɛj],
communément [ko̞mynemɑ̃],
forêt [fo̞re̞],
gomme [go̞m],
ordinateur [lo̞ʀdinatœʀ],
corps [ko̞ʀ],
cochon [ko̞ʃɔ̃],
Cambodge [kɑ̃bo̞dʒ],
donner [do̞ne],
époque [epo̞k],
Europe [øʁo̞p],
homme [o̞m],
comme [ko̞m],
comment [ko̞mɑ̃], etc.

French ɔ (open oh) (ɔ as in awkward); (more open oh)
................ OR (ɔ as in for) [o̞] (less open oh),

Answer 1

As a beginner, you really shouldn't worry about this. Just consider the open and closed "o" and you'll be fine.

The pronunciation of "o" in particular is heavily dependant on accents so there isn't even a right answer. Some open "o"s can be slightly less open depending on various things like position in the word, position of the word in the sentence, general mood and intent of the speaker, etc. but there are no rules for that.

With time and after listening to enough spoken French it will come naturally.

Answer 2

The symbol always signifies the same sound, so the ɔ always has an ɔ sound. What you're asking I think is what letters have this or that sound. The o in soleil and most of your examples is the short u, represented as an upside down v. When followed by an r the o is ɔ. The o̞ is in 'haut' and words ending in -ot, etc. Many of the French vowels are grossly and bizarrely misrepresented in phonetic transcription. Do not pay attention to that. Pay attention to how they are actually pronounced.