The aerial tubers of winged yam are said to be edible, but they are generally quite small and once peeled probably would not leave much edible tuber. I prefer the underground tubers myself.
The underground tubers are collected in the winter when the upper vine dies back. If you collect them the first year they are generally about four inches across, but if left for a second year they can become much larger. I prefer first year because they are smaller and easier to dig and handle.
Some folks have recently been photographed with thirty pound tubers, which are probably many years old. I would think the older tubers would be pithy, but I can’t say for sure as I have not tried them. Plus, I prefer to collect what I am going to use rather than try to store a thirty pound tuber.