How would you deal with a subordinate who has a constant strong body odor?

I've never seen this be an issue as far as letting the SM know. It typically went something like "Hey sh*tbag, you f**kin smell like sh*t. Go scrub your @ss!" And at other times it wasn't phrased this politely.

Probably not the most PC answer but I had a Soldier in Iraq that refused to clean up, whether its using baby wipe baths or bottled water. It got so bad I threatened to use simple green and a toilet brush to scrub him myself. Needless to say he was powder fresh the next day.

Interested to hear the feedback here...Early in my career, I worked on a hospital unit and had one of our more seasoned RNs tell me that my perfume was too strong and could really bother someone around me who is allergy or migraine sensitive. I was kind of shocked as it was light scented, but didn't realize until years later (and suffering from migraines myself), just how offensive and disruptive another person's smell can be. I think it's fair to politely pull someone aside and mention that it's noticeable and a bit distracting...or worth sharing with HR if you're not in an appropriate position to provide such feedback.

Ask if they have a medical condition. If they do not know, tell them they should get checked out. If it turns out they do NOT have a medical condition causing this, then instruct them that they need to shower daily. Maybe even twice daily

When I was cadre in AIT-land, we had our fair share of Soldiers who lacked proper personal hygiene. Without being too invasive, I asked how they were raised when it came to personal hygiene. Get to the root of the problem and you’ll be able to give the proper guidance on how to correct it. In my experience, more often than not, they really didn’t know any better.

LTJG (Join to see) ,
Be honest, direct, and as kind as possible. Start by mentioning that he/she's work has been good (assuming that it has been) and then say something like, "I want to discuss something that's awkward, and I hope I don't offend you. I have noticed you have had a noticeable odor lately. It might be a need to wash clothes more frequently or shower more, or it could be a medical problem. This is the kind of thing that people often don't realize about themselves, so I wanted to bring it to your attention and ask you to see what you can do about it."

(Note that you're saying "I have noticed," not attributing it to the complaints you've heard. That's deliberate, in order to contain any resulting awkwardness the subordinate might otherwise feel toward others.

Likely, the subordinate will be embarrassed. But if this person is resistant or combative, explain that they do need to come to work smelling fresh and clean because of the impact on the others.

Also, be prepared for the possibility that you'll hear that there is a medical reason for the odor. If tells you that's the case, then at that point there's not much further you should do, other than thanking he/she for telling you and reassuring that you'll of course accommodate ,now that you understand it's related to a medical condition.
Hope this helps.

I've had to supervise showers & laundry for a particularly nasty and wholly unclean shipmate who just wouldn't do either unless ordered and supervised to... absolute dirtbag (pun intended)

Verbal instruction first. That can be as informal as possible or filled with expletives. Which ever works. There have only been a few instances where I had to resort to "forced bathing." Which is something I have had to do in the civilian world more than in the military.

1960, France, Engineer Company, hard working, hard smoking and denouncing of misfits. If ever there were some. One soldier refused to even wash, a slap of water on his face in the remote latrine was the most he ever managed to do. Uniforms and civilian clothing were dumped in his wall locker. Early did the clothing get sent to the weekly laundry run. Now although it is needless to be stated, by it will clarify any questions running through any minds. Yes, he did stink to high heavens, so bad the squad leader had him stand in the rear of all formations. Instructing him to bathe and peering it did no good. A G U wash party as former consisting of volunteers from throughout the company. The man was called in English, Fish head, because the odor was similar to rotting fish. In French it is, there a pouison, or close to that. The poor man was scrubbed with the old wooden handled toilet brushes and the brown issued soap. It was done in the shower room, all over in ten or so minutes including the time down disrobeing him. Nothing changed except his skin color, he became pure pink and red, a far cry from his natural black skin. The G I party was well intergrated, and had the approval of most of the company. Our medic kept him salved up until he didn't t need it anymore. He was an amusement to us due to his putting on black market moustaches and sideburns and grabbing civilian clothes off the dirty pile in his locker. He,'d go downtown and chase the ladies.

I worked with an Airman once whose body seemed to have its own ecosystem (yes, yes, I know on a micro-level our bodies are pretty much self-contains ecosystems, it's metaphorical). He would come into work at 0700 clean-shaven, but by 0930 would have enough shadow to bust the AFI and would have to go shave again; dude shaved four times a day to keep the SNCOs off his back. He once came off two weeks of leave and legit had a beard past his chest.
He also had BO like nobody's business. He actually had to use antibacterial soap, the kind they use before surgeries, to shower, but I have no idea if he kept missing a germ or it lived under his skin, he'd start shift smelling like roses but even just sitting still for an hour would develop a marathon-runner style odor that cleared out our section.
I actually felt bad for him. He was taking every measure possible to keep himself clean and in regs and everything, but he couldn't go two hours without turning into a dirtbag.
It came to a head when the Director of the NSA visited our watch floor and it was at just the wrong second, he passed by this dude and commented to the Group Commander about it.
We all knew his troubles and we sympathized with him, but after a three star tells a full bird that his E-4 is a pile of sh*t, there's not much you can do to save him. A week later, he went to mental health saying he had suicidal thoughts, and about two months after that was discharged from the Air Force.

The reason I tell that story is that, well, are you sure he's not already well aware of it and in fact is already doing his best to keep clean and pleasant smelling, but he just simply can't?