I feel like I should weigh in on this from a management point of view.
I had an employee who stank. A couple of them, actually. One was the typical basement-dweller who'd occasionally turn up unwashed, probably because his World of Warcraft raid went longer than expected. The other, more frequent offender was a middle-aged woman who regularly went up to a week without showering/washing her hair, and I'm not sure her clothes were ever cleaned.
Although I noticed on occasion, I never thought it was the end of the world. A bit unpleasant, but what can you do? Then again, I had my own office. I only had to be up-close and personal for very brief periods, a few times a week. I didn't have to sit a few feet away from them in a rather stuffy, completely open-plan office. So when other employees started to complain, at first I thought 'what is this? high school?' I suspected that a lot of the complaints stemmed not from actual hygiene concerns, but from the fact that these two individuals were also just incredibly awkward and annoying. (And in the case of basement-dweller, I do think that was 90% of it.)
I admit that I took a while to deal with the situation, partly because I was swamped with issues that, frankly, seemed a little more pressing than B.O., and partly because I really had no idea how to tackle the issue.
The trouble wasn't really basement-dweller. As I said, he wasn't really the habitual offender that people made him out to be, and even if he had been, I could have looked him in the eye and said 'dude, take a shower,' and not only would that have been sufficient, I don't think he would have been especially offended or embarrassed. The problem was the middle-aged lady. I knew that she'd been homeless in the not-too-distant past, and I really didn't know what her current situation was. I felt it was entirely possible that she didn't have hot water, or soap, or money for laundry facilities. I also knew that she had a history of filing complaints against employers for discrimination, unlawful termination, etc. Now, since she was a temp (they all were), I could have solved the whole thing really quickly with a single phone call. But we were absolutely drowning in work, she was at least reasonably competent, if rather slow, and she happened to be the only means of transport for her niece, who was one of my team leaders.
So, in the end, I sent a memo to everyone, naming no names, but laying down guidelines for hygiene. I also made it clear that shower facilities were available for use in the company's on-site fitness centre, and that soap, etc. could be made available.
It worked...-ish. Things did get better, but there were still some days that were rough. Mostly, I thank God they shut the product down and I didn't have to deal with any of them any more!
So, the moral of the story? Even though your manager sounds like kind of an ass, it's not actually always as easy to deal with something like that as you might think. By all means, if you can speak to someone in HR, go for it. They might be able to do something. But at the end of the day, I wouldn't hold my breath. Or, you know, get used to holding it.