Try placing one plate in the sink, adding a couple of tablespoons of vinegar, and stacking another plate on top (replacing the air between the plates with vinegar). Let sit for a couple hours, then hand wash and let dry. If the smudges are gone from the side of the plate that contacted the vinegar, they are water/detergent stains and can be removed by following that procedure with all your plates.
You can try the same thing with a product such as CLR.
Another thing to try is put a plate in a basin slightly larger than the plate itself. Barely cover with very warm water and add 3–5 denture cleaner tablets. When the foaming has completely stopped (or overnight), wash and let dry.
Finally, I have had water spots from a dishwasher that were only removed by repeated hand washing. I bought a set of crystal glasses for re-sale and I was very disappointed when I couldn’t get the water spots off. They were so nice I decided to use them for every-day. After a week or two, (I didn’t own a dishwasher) I noticed they were spot-free.
If none of these methods work, your plates are almost certainly permanently damaged. I’d suggest buying new plates and either not storing them in a drawer, or keeping something between them, such as a coffee filter or paper plate (both of which can be reused time after time).
Good luck!