I've used Simple Green under the hood many times, I use it on alot of stuff actually. Oven cleaner does work pretty good for slimey valve covers or small oil leaks as long as you hose it all off, I try not to use Gunk but do when necessary. I try not to simple green belts though, it makes them squeek if you get them ..squeeky clean.. but a black crayon or a little bit of wax will quiet a squeek. Soap and water work best on regular dirt if you can get to the places you want to wash, if not spray Simple Green on it and hose it off.
I ned to do under the hood of my current project so I'll do before/after pics and post what all I use to make it shine.