As a city dweller, I get my wood ash from a local pizza shop that uses wood fire ovens.
Note - the ashes from natural, untreated hardwoods are generally preferred.
1. Make Soap - the ashes from hardwoods can be used to make lye water, which is a primary ingredient in homemade soap. You can make lye water by boiling hardwood ashes on a stove top or by constructing a lye leaching barrel. Note that lye water is caustic, which means it can burn like acid, eat through certain types of containers, should be treated with extreme caution, and used in well ventilated areas while wearing appropriate safety gear. Lye water plus animal fat makes soap. One article that has stood the test of time (it was first published in the 1970s) explains the basic, no frills process for making lye water, and then soap, from hardwood ash. Check it out at: http://www.motherearthnews.com/homesteading-and-livestock/how-to-make-soap-from-ashes-zmaz72jfzfre.
2. Neutralize Odors - from the litter box to the dumpster, there are plenty of places where you can sprinkle hardwood ash to neutralize bad odors. A small bowl of hardwood ash can be used like baking soda to absorb odors in refrigerators. Replace every few days.
3. Remove Oil / Grease Stains - hardwood ash can be sprinkled over stains on porous surfaces like asphalt, cement, and stone. Let the ash settle for several minutes, then sweep away with a broom. Deep stains may require longer settling periods and further treatments.
4. Polish Silver and Glass - mix a small amount of wood ash with water to form a thick paste. With rubber gloves, apply a dab to tarnished silver or cloudy glass, then polish and wipe away with a clean cloth. Be sure to test on a small portion before applying to an entire surface.
5. Pest Control - sprinkle a pinch in corners, in the backs of cupboards, and across thresholds leading to the outside to deter pests like ants, cockroaches, mice, and rats.