Can I use firewood ashes in the veggie garden?

yes....sparingly.

if you compost them it would be OK, eventually, but water and wood ash creates lye, which would burn your plants.

I do believe it will make the soil more alkaline, is this what your plants need? I would check gardening sites.

I would add it to a compost pile and let it break down before using it directly on your garden. The variety of wood could cause damage to your plants otherwise.

Most firewood ashes are high in alkaline. That might be OK if your soil has a high acidity PH but if the PH is good or slightly positive then that would not be a good Idea. BTW, The pioneers used to make Lye from rainwater filtered through oak ashes. Lye is a very strong alkaline.

Absolutely yes as long as there are no plastic or other foreign matelial being burnt. Be aware that printed newspaper has chemicals in the ink. Wood ash is the missing ingredient in the soil nutrients because of the deep root system trees have, thus transfers into the soil. Harvest your ashes while they are still a bit chunky.

You can use them around black walnut trees, and to get flowers to change color, or to kill plant growth in a certain area, but I think it would ruin tomatoes. Composting is best, or maybe a small hole you want to fill. It will take many pans of ashes to fill a hole, but it might solve two problems. Best wishes 😇

Yes, They contain potassium, aka pot ash. Here's a link about it.

http://www.gardensalive.com/product/using-wood-ash-wisely/you_bet_your_garden

I am posting a link below that should be very helpful, but first some basic info from it for you to peruse:

"... good quality hardwood ashes—that means no ashes from BBQ grills, cardboard, plywood, painted, or pressure treated wood—do have real agricultural use. (Softwoods have a lot less value, but you shouldn't be burning soft wood in a stove or fireplace anyway.) The best information on how to properly utilize the valuable material in wood ash is contained in a couple of great farm-scale articles from the Georgia Extension Service and the government of Alberta's department of Agriculture, Food and Rural Development. We'll post links to those articles at this end of this Q of the Week for those of you who want all the details. ... ... So the first thing you need is a soiltest. I know—I always say that. And I'm always right! This time double, because you'll be using those ashes to actively change the pH of your soil and you need to know where you're starting from. ... ... "

http://www.gardensalive.com/product/using-wood-ash-wisely/you_bet_your_garden

http://www.naturallivingideas.com/wood-ash-uses/

https://www.thisoldhouse.com/ideas/10-uses-wood-ashes

Wood ashes are a good addition to compost- decomposing matter raises the acid level, and ash is alkaline. If you add a lot of ash to your compost, you may not want to use it on acid loving plants like azaleas, etc.

My grandmother always put the ashes from the stove on her garden during the cold months.

We do.

thanks!