You can wash a quilt in a top-loading machine, but you *cannot* let it go through an agitation cycle! Stop the machine before it starts agitating and just use your hands to push the quilt up and down in the soapy water. Move the control to "spin" to get rid of the soapy water. Do the rinse cycle(s) the same way. The spin cycle is gentle enough to use on quilts; machine agitation is not.
The quilt should be laid out flat to dry. If you do this outside, place a large sheet both underneath and on top of the quilt (on top protects from bird droppings) and anchor the corners with stones. It is best to do this in the shade to minimize exposure to sunlight, which fades fabrics. If you don't have a shady spot big enough, I would put extra sheets on top and try to keep it out of the worst sunlight of the day. You will probably need to turn the quilt at least once.
Never hang a damp quilt on a clothesline. Water is heavy, and the extra weight of water in the quilt will put undue stress on all of the seams and quilting lines (not to mention the exposure to direct sunlight).
If you don't have a suitable spot outside, you can dry a quilt inside (carpeting works well). Again, lay it out on sheets. In this case, add a fan to speed drying, and plan on turning the quilt occasionally.
Dry cleaning is really not particularly good for quilts. I wouldn't do it.
Orvus is the soap usually preferred for washing quilts. If the quilts have spots or staining disfiguring them, you might want to use Retro Clean. The process for that is a little different. Here is a link to Retro Clean:
http://www.retroclean.com/