I would be cautious about washing any glazed ceramic as it may have small cracks in the glaze. getting it wet could drive dirty liquid into the cracks and cause staining which is difficult (and sometimes impossible) to remove. Even relatively modern glass can respond badly to being soaked, depending on its manufacture and previous history.
Do you know what the dirt/deposits are? Why do they need to be removed? Is there any way they could be an interesting part of the objects’ history that needs to be retained? At the least they may retain DNA from previous users, remember. Not everything needs to be shiny and clean. If you are sure this is dirt from inappropriate storage and really does need to be removed, then read on.
I would start out by examining each item in a good light to see if there are any cracks, areas of weakness or surface damage that might cause problems. Then I would prepare a safe area to work on the items where they can be handled, cleaned, allowed to dry etc, safely, with minimum risk of them being damaged. For example, pad a table top with a towel or several layers of paper towel so that if an item slips it will not fall on a hard surface. Make sure items cannot easily roll off or be tipped over, especially if other people come near the area.
Experiment on a small inconspicuous area first. Keep observing the object while you are cleaning it. Expect the unexpected and be ready to stop!
I would use distilled water and a soft microfiber cloth to gently wipe off the surface dirt without wetting the surface too much. Don’t wipe the dry dirt across the surface as it may be scratchy. Work on a small area at a time and allow yourself enough time to finish one item completely. Try not to leave an item partially cleaned as it may develop a tide line. Clean the cloth often so you are not wiping dirt over the surface. Allow the item to dry on clean paper towel and change the paper towel occasionally.
If distilled water alone does not remove enough of the dirt, then I would move up to a non-ionic detergent. Soap and normal commercial detergents can leave deposits which are not good for the object. University Products in the US sell TritonX-100 http://www.universityproducts.com/cart.php?m=product_list&c=1171 while in the UK we would use Preservation Equipment or Conservation Resources as a supplier.
Use the smallest amount of non-ionic detergent possible, mixed with distilled water, and gently wipe the surface clean. You can even just dip the microfiber cloth in the foam of the detergent solution to minimize the amount of liquid on the surface. When the dirt has been removed, switch to distilled water and wipe off any remaining traces of detergent solution. Allow to dry on paper towel as above.
Be cautious, test first, and be vigilant for an object trying to misbehave. Take photos before and after and record exactly what was done, what was used and when – this is all part of the objects’ life story.
Hope this helps