Well oxygen is the key. As long as you provide a way that gets oxygen to the worms, individually, they are going to be alive. If you wash the worms in tap water, chlorinated or not, until there are no dead worms or stuff, you got clean worms. Clean worms stirred up in clean water settle in a couple minutes and you can drain off the extra water. The key to providing oxygen to the worms is the water level and amount of surface area of the container they are in. A plastic shoe box or sweater box works well for me. I can clean the worms in this box with the spray from the sink, not the kitchen sink. Let the worms settle out, drain out the water until there is less than an inch of water left. Worms in this set up can be kept for a couple days at room temperature (68 to about 75 F) without aeration. In a sweater box you can keep about a quarter pound. If you cool them off in a refrigerator (40F), you might be able to go a bit longer or store more worms in the same space.
Another way to keep worms, if you have a sink that you can allow the water to run at a slow stream all of the time, you can do the following. Place the worms in a 10 gallon tank. Fill with water. Stir up the worms daily. Let the cold water run into the tank and overflow to the drain continuously. I know a number of public aquariums that use this method. The downside of this is if your water contains a high level of chlorine, but it still might work since the chlorine might be consumed by the effluent from the worms.
A third good method is to put the worms into a tank that contains a deep layer of gravel or sand and no fish and a good filter. Basically the worms will stay alive in almost any tank set up for your fish, if only the fish would not eat them. In a 30 or 40 gallon tank set up for fish but containing no fish, and a good layer of gravel, the worms will spread out in the gravel and stay alive and even reproduce for as long as you maintain the tank like you would a fish tank. It is a bit more trouble to collect the worms to feed them to fish.
