The amount of water has to do with the stocking density. In a 10 gallon I'd start with 1/4 pound, it's an amount slightly larger than a golf ball. A sponge filter provides bio filtration, keep it suspended off the bottom, as they will go in there. You've got a small amount of worms in a large container of well oxygenated water, so O2 isn't an issue.
If you keep them in a refrigerator you can keep 1/4 pound in a sandwich size tupperware container, much smaller than a 10 gallon tank. You'll want to keep them in as little water as possible in this setup, so they do have access to O2, the surface where they contact air. The amount of water in this container would be measured in ounces, no where sufficient for that stocking density, and the refrigeration slows metabolism, nearly the same as pond fish work in the winter.
If you want to culture them there's no reason why you can't downsize the 10 gallon idea, a 2.5 gallon & 1 ounce will work. With a culture expect it to double every 4-6 weeks. This is commonly done by folks who don't have access to a shop or someone else selling live blackworms.
Seeing as I sell 50-75 pounds a month you can imagine the setup I'd need to cultivate them, there is no way I'm doing that. I keep 5 pounds at a time in 12"x22" food grade bins, rinsing & draining daily, no different from what you'd do with a small container & 1/4 pound. Get in 25 pounds, rinse & stack bins in a beater fridge in the basement, rinse daily & sell as needed. Here's a little info should you choose to go that route, or need to store some that you've cultivated;
Organic Blackworms - Blackworm Care