Barbara, The sonic cleaner sounds cool, and is probably the closest thing to a cleaning fairy, but perhaps you are not into gadgets, and are looking for something simple and low-tech, and above all, handy.
In my college days I cleaned parts in my dorm room sink (sounds horrible, doesn't it?) using concentrated ERA liquid laundry detergent, same as I used for doing my laundry. Of course I'd first wipe off excess grease with a paper towel, but I was amazed at how effective this detergent, water, and an old toothbrush were at cutting grease.
I believe Dawn dishwashing detergent is used these days for cleaning the plumage of seabirds caught in oil spills, so it does cut grease while not being as nasty as petroleum-based solvents.
Another trick I've used more recently is toothpaste on an old toothbrush. Not so much for degreasing, but for cleaning up rubber, plastic, aluminum, and chrome parts that are just dull and grimy, and lack that showroom sparkle. It seems to work, and again is water-soluble and right there by the bathroom sink. I like the whitening kind; I think it has some mild abrasive and bleaching properties.
No, I'm not joking. It may be dumb but it's what I do. Of course, I'm talking small-scale jobs, not a bike shop.
Austin, Texas, USA