I think it's something to do with the starch on the surface of the noodles. Do you rinse them? -- which also helps to stop the cooking. Also, try using a vinaigrette instead, and mixing it in while the pasta is warm. You can add veggies etc. after it's all cooled down. Better for you than mayo, anyway.
As for soup storage: if possible, cook and store the noodles/rice separately. When you add them all at the early stages, they can overcook just from being in the hot liquid as it cools down. And of course reheating the whole thing makes it worse. Cook them separately and just add them to each portion as you need to. It also helps if you undercook them a little, so that when you heat the soup, they finish cooking.
As for soup storage: if possible, cook and store the noodles/rice separately. When you add them all at the early stages, they can overcook just from being in the hot liquid as it cools down. And of course reheating the whole thing makes it worse. Cook them separately and just add them to each portion as you need to. It also helps if you undercook them a little, so that when you heat the soup, they finish cooking.
