Wood ashes may be helpful or harmful to your garden depending on your soil pH, acidity. Wood ashes are strongly alkaline (the opposite of acid) and historically were used to make lye for use in soapmaking.
Your garden needs a pH of about 7, which is neutral. In Michigan, we always added wood ashes to the compost or directly on the garden to "sweeten" the acid soil. When we lived in Texas, the soil was already strongly alkaline and needed acid forming ingredients added instead of the alkaline ashes.
There are a number of test papers available at a pretty good price, including litmus paper that turns from blue (alkaline) to red (acid) and back again. If your kids are in chemistry class, they could ask the teacher if they can take a couple of strips home. The diabetics among you may have urine test paper that is far more accurate and expensive, that turns from yellow through chartreuse to green, and has a color chart to match for a reading. And there are other test papers. Ask your pharmacist.
A homemade test is to add a little beet juice (NOT pickled beet juice nor harvard beet juice, both have vinegar added!) to distilled water, just enough to turn it pink. Add a pinch of ashes and it should turn blue. Take some more pink water and add a little garden soil. If it stays pink, the garden needs ashes. If it turns blue, don't add ashes to the garden.
I used to be an Extension agent. ;-)