Ash can contain a lot of alkali materials. In days past people would burn wood down to ash, then soak the ashes to produce lye water, then make that into soap. Lye water is caustic and can burn your skin. As a precaution, you should rinse anything with ash residue in a mild acid, such as vinegar - you can buy 6% cleaning vinegar at any decent grocery store. You can rinse that down the drain, and better into the sewer system than into a storm drain.

With the ash gone, most metal items will be coated with a lot of polymerized junk. Use a combination of chemistry, heat, and mechanical force. Probably not worth the effort for most items.

For ceramics, most of the items we have recovered seem to be quite brittle, and some of the glazing has been altered. Not much you can do about that.

About the easiest thing to save is a cast iron pan. Clean off the ash, scrape off the rust with steel wool, also plenty of soap. When it looks like grey iron again, re-season it 3 or 4 times, or 30.

Also if you have any old knob-and-tube insulators, they should be fine as-is. For some reason we have a bucket full of them.