I was shocked to see this symbol[ɔf] for of and hear the produnciation. Do the British really pronounce "of " as ɔf? I have always heard "əf" and when I heard Korean students pronounce [ɔf], I corrected them.
By /ɒv/, do you mean /ov/ in AmE?
I mean the sound when you should round your lips into a small tight circle. The /ɒ/ is only used in the British pronunciation systems, I guess. The reason why I haven't heard /ɒv/ for "of" is, I guess, they rarely pronounce so even if they do.
The first variant is possible, since it falls under the CLOTH lexical set. In some accents, both CLOTH and LOT are merged. Same with with BATH and TRAP lexical sets.