I suppose it's possible that people could feel worms throughout their body. But there may be other explanations as well.
For instance, nutrient imbalances. The neuromuscular system relies on potassium, calcium, and other ions which are responsible for modulation and control of action potentials, or impulses, in the muscles. This actually goes for smooth muscle too, which you find in the intestines, blood vessels, and elsewhere. Anyway, imbalances in these nutrients can cause "fasciculations", which basically feels like a fluttering in the muscle. Severe imbalances in calcium or potassium can actually lead to irregular rhythms in the heart, aka- arrhythmias. In severe cases, these can be fatal. But in mild cases, you might just experience these fasciculations, which could feel a lot like worms running around your body.
Incidentally, several parasites, especially intestinal worms, can cause these nutrient imbalances because they steal nutrients or disrupt absorption. So one could have a firm diagnosis of worms - ascarias for example - and feel these fasciculations and come to the natural conclusion that the worms are all over their body and not just cycling through the GI tract to the liver to the lungs and back to the GI tract per their norm.
Someone else mentioned that they feel worms inside their cranium. Some parasites definitely make it in there, such as a bad case of entamoeba histolytica. But this is usually rapidly fatal. The only way into or out of the cranium is through narrow foramina (holes) that are passageways for blood vessels and nerves. There isn't really room for a big worm to crawl into or out of the cranium. Not to say that something else weird isn't going on, but I'm not sure the worm hypothesis is the only answer.
The question comes to mind... then why do these zappers seem to help? One answer would be that electricity stimulates muscle and rapidly fatigues it. This temporarily resets the neuromuscular pathway, rendering it incapable of fasciculating for a while. So this could seem like you zapped something and it moved away.
Of course, this is not to say that no such thing could ever happen. Certainly worms can take up residence in muscles or other weird places in the body. But there are other explanations that could also be considered.
As for the movement around the belly button, if you're quite skinny, it's possible what you're seeing is the pulsation of your abdominal aorta, which is a very large blood vessel in the abdomen. Really, it's pretty huge. The pulsations would likely be somewhat regular when they occur, but could definitely come and go with changes in blood flow dynamics or alterations in the autonomic nervous system - such as bowel motility, emotional changes, etc.
Or it could be the fasciculations of smooth muscle in the intestinal wall.
I've had these fluttering feelings myself, and it honestly feels like worms wriggling around, and who knows... maybe it is. But I think these other explanations also merit some consideration and are certainly possible. I started thinking about it because one of my blood tests showed that I'm mildly hypokalemic (low blood potassium). If you get a standard "chem panel" or "chem 7" or "blood chemistry panel" with your blood work it includes these kinds of things. It's pretty standard, but if it's only mildly depressed or elevated, your doctor may not think much of it.
But I would look very closely for any lab value that's out of the normal range, even if it's slight. There's usually some clue there that can help answer at least some of the questions we face.