The weakness is another variation of the fatigue, I suspect, and similar to a CFS "crash". I've experienced it several times where I barely had the strength to get out of bed, or, while seeming "normal", could only exert a fraction of the effort I normally can at, say, an exercise bike.
From my research I believe it all centers on the "reticular activating system" in the lower brain. This area modulates arousal and alertness and mediates the production of many neurotransmitters. It's likely that this area is damaged in the initial polio infection, and over the years what little "reserves" it has are used up.
Certainly problems in the neck area can affect, eg, the vagus nerve that controls much of the "innards", including breathing, digestion, some control over heart rate, etc. But the neck problems and RAS problems are unlikely to be connected except that they could both be triggered by polio.
Another "neck problem" that can occur (and which is fairly controversial) is "Chiari malformation", a condition where the lower back section of the brain has slipped down into the neck cavity a bit. This is claimed to be responsible for some cases of Chronic Fatigue, and many people have had surgery to correct this. Success with the surgery has been hit-and-miss, however.
I have for years taken Strattera, which enhances the action of the neurotransmitter norepinephrine. This totally vanquished my fatigue. However, the side-effects of that were too severe to permit a full dose, so I recently (about 5 months ago) switched to Intuniv (a long-acting form of the BP med Tenex). It works differently (actually through the RAS, I gather) to enhance neurotransmitter supply, and it has essentially zero side-effects (other than lowered blood pressure, which for most of us is a blessing).
So far I'm taking a dose of Intuniv that doesn't totally eliminate fatigue (works about as well as the low dose of Strattera I was taking last), but I have the Dr's OK to up the dose in the next couple of months (once this shoulder thing is cleared up, so I can more accurately judge the effects).