Don't be mistaken, your boss probably knows he is having these issues as well. I used to have pretty severe social anxiety (and still do to this day, albeit to a lesser extent) and I would think about every little thing "wrong" with me during the day. I tend to sweat a lot when it gets hot and I would stress endlessly about the sweat on my armpits. Other than turning on the AC, there wasn't much I could do. My solution for this would be to preemptively turn on the AC onto a cooler setting at the start of the day.
Note: Ask your colleagues before you do this to make sure they are OK with it. I would recommend against expressing the real reason behind why you are doing it. Just say that you are too hot or something along those lines.
As for the bad breath, I would chew some strong, minty gum if I ever found myself forgetting to brush my teeth. If you can't stand his breath, take some out and chew some yourself and ask him:
Hey, do you want some gum as well?
This is less direct and in my opinion more professional than flatly commenting on your boss' breath. After a while your boss might get the hint, or he might not. In the case that he doesn't get the hint, you should be more direct.
Take him aside and let inform him of his hygiene issues in a polite way. Don't make any rude comments or spend a long time dwelling on it; just get to the point and express how you think his hygiene might be impacting your relationship with your clients. The case may be that he just doesn't realize how bad his breath smells or how much he is sweating. I would greatly appreciate it if someone told me I smelled if I didn't realize.
Edit 1
In response to your comment where you state
I really can't take him aside to tell him, I would be too much embarrassed
You could try placing an anonymous note on his desk instead of directly confronting him. This saves you the embarrassment from having to talk to him face to face about the issue.