I have always had good results with solvents sprayed on a cold engine + surrounding areas, letting it work for ca. 10 min., then followed by steam cleaning. Afterwards the old elbow grease: Rags, brush and solvents.

To me, it's important not to stop there though. Now that I have a clean and eventually also dry engine bay, I have to assume that all rust protection and lubricating oil is gone. So I give all linkages etc. a treatment with the oil can, and wax all painted areas in sight, particularly around the body seams. The result also makes it a lot easier to keep the engine clean, I just hose everything down when doing the weekly wash. An easier alternative to wax is to go over the seams with a spray can of Tectyl (or similar) universal rust protection, but I like the glossy, like-new impression the car wax gives me. I also use plastic/rubber chemicals on the hoses and cables. Doing this once a year gives me an engine looking like this: