They are directly related to the state of physical health, but sadly are not the only thing directly related. That is the reason why when you read about most mood swings disorders you find points like "healthy food choices" and "exercising" but sadly they are not the only points, otherwise things would be much easier.
This is depends on the individual. For a person establishing their relationships in a changing world and is trying to determine who they are, where and how they fit in, health and vigor can be key to good self esteem and thereby emotional stability. In an older individual, with a "few" miles on them. Lack of vigor and poor health in general may be a best case scenario. They may well be quite stable emotionally and possess great wisdom.
In general, since the psyche is enveloped by the body ( and the body is a necessary part of the psyche) good physical health (fitness, diet, saying "no" to drugs) should be pursued as part of overall a pursuit of clear mindedness and a stable emotional life.
Curiosity about ones own unconscious content is equally important. When you see or hear something that gets under your skin, that is a red flag indicating a piece of your own shadow that, if you can bring it out and integrate it, can lead directly to a better self understanding and more emotional stability.
Aside from obvious mental illness, you get many people who are of a hyper healthy physical health, but are the worst kind of people. I had a former friend who ate all organic, never ate refined sugar, and barely ate any sweets at all, no red meat (I debate how necessary that actually is to being healthy), took no legal or illegal drunks and didn't drink or smoke. He ran every day and was constantly moving an active.
He was the biggest jerk I have ever met.
Also completely needy and demanding while giving nothing back, not even trust.
So even if he was "balanced" inside and out, he was still a massively messed up person.
I still believe healthy body does lead to the healthy mind though.
whenever I'm in a bad mood and don't really know why, or just don't feel as happy & energetic as I want to, I blame it on something I ate. maybe I'm totally wrong about it, but it makes me feel a bit better at least.
Everything is inter-related and they influence each other. The question here is what is health?
For example, when I get myself too fit, as in, too strong, then I also become more aggressive and reckless than I feel to be useful for me. It's true, I've tried that. In fact, my most intellectually efficient times, I've been maintaining extremely unhealthy body by all usual standards. Then, which is which.
I'm certainly not convinced that maintaining the types of body that TV/media/fashion/art promotes, is necessarily the best for your brain. At least, this issue deserves serious consideration.