lightly dilute in a bucket with warm water first, you don't want a soapy residue leaving streaks .... and lots of elbow grease, wax on, wax off. Sometimes multiple applications are needed.
Believe it or not Totally Awesome cleaner works very well both in the shop and the house. $1.25 a bottle at Dollar General. I bought 10 bottles just yesterday
Rattle can wheel and tire cleaner works well. Spray it on and let it do its thing. No real need to rinse it off because it leaves a nice “just detailed” look including belts and hoses. Use it somewhere that drips don’t harm the floor or use a drop cloth or tarp to catch them. Do as many times as you want until you get the level of clean you want. This is what the “professional” detailers use.
For my "driver" Model A, I used to wipe down the engine after each drive using Crocodile Cloth wipes. They are excellent at removing any road residue, oil, etc., and they're also great at cleaning hands! I keep a container of them in all of my cars and in my shops as well. I buy them at Home Depot.
If you don't have an air compressor you can use a leaf blower to blow things dry under the hood. I would put plastic bags over anything that you don't want wet.
When I was going to detail an engine compartment on a car to sell I'd use oven cleaner. I'd spray it on drive to the quarter car wash and spray it off when I got home it had dried and was clean enough to paint.