Are you repainting the engine bay, IMO, if you are going through the trouble of cleaning it, may as well detail it. It looks so nice with fresh paint on it. But I am crazy about this stuff, I can not count the cars that an exhaust system turned into dropping the tank and painting the entire bottom.
Just to clean it use a product called zep purple
http://www.homedepot.com/p/ZEP-5-Gal-Industrial-Purple-Degreasers-ZU08565G/100619267 hoe depot by the 5 gal jug, the "zep guys" used to come by my shop every 2 weeks years ago, they stopped that and now you can get the stuff at the depot instead. Works well, better than the gunk foaming shyte.
I have a hotsy pressure washer with an oil burner on it, for steam cleaning, and you can rent them.
If you are willing to repaint under there and don't have a sand blaster, grab a cheap speed blaster, I love them things, I have like 4 of them, awesome for a little job like under the hood. It doesn't cost much even if you don't have the tools as long as you have a compressor.
qt of ss urethane, primer, cleaner, cheap spray gun, masking tape, sand, speed blaster, etc maybe $250 total and it will look great under there.
If the motor is out I can do it in 4 hours, then let the paint dry.
I do stick to purple zep for under the hood and a hot washer works best, grease seems to harden back up when cold water hits it.