What is the usage difference between these three definitively? As an intermediate Japanese speaker, I somewhat understand where I would say them, but I can't point out under which contexts any of them "wouldn't be allowed" compared of any of the others. In speech, I have no problem selecting one for usage, but I just can't pick out if, when somebody else uses one, they are using it in an "incorrect" way (I can figure out if it's natural or not).
〜が is largely a "but", where you give a contradicting statement afterwards
〜ても is closest to an "even though" suffix to a word
〜のに is a more emotional "が", with a connotation that even though an action was taken, that something has / hasn't happened.
Where is each NOT allowed under the other contexts?