OP,
Whatever you do end up saying to him, I think it's initially best done quietly and in private.
Defences will go straight up, if he feels publicly humiliated and the object of group discussions.
(And apparently can even lead to bullying accusations).
You'd also feel guilty, if it then transpired he is battling a serious medical condition and genuinely unaware of the toxic breath.
Or possibly medication for something is itself compounding an existing problem: e.g. severe nausea side-effects preventing him from daring to eat/ drink at work...dehydration...biochemical change.
Though, of course, the responsibility would lie with him to flag that up and get assistance from his Dr...certainly not much comfort to you on the receiving end, being made to feel physically ill too.
[PP mentioned the old nurses' trick of dabbing Vicks in each of your nostrils: can confirm that does help (assuming you like its smell?!)]
If, after your conversation, he doesn't then take on board how unpleasant it is for you all, or refuses to up his efforts to tackle (or at least mask) the problem straightaway, then you've got no other option but to ask someone senior to deal with it.
It's pretty unlikely, but he could also just be one of those selfish eejits who is only too aware his personal hygiene's disastrous, yet simply doesn't give a toss about anyone else's wellbeing enough to improve.
You'll find out either way, once you have a word.
Good luck; it's really awkward for all concerned, isn't it? 