There are a few different ways of approaching the cleaning of your engine bay and this depends on how aggressive you want to get. In most cases, simple wiping down of the surfaces with cleaner and rags may be sufficient. In more severe cases, you’ll need to use stronger chemicals along with agitation with brushes, and then wiping away or rinsing away with water.
One of the worst feelings you can have is driving a car with a sticky steering wheel. Personally, I’ve driven company vehicles for my day job with several that were more than 10 years old and have been changed hands many times. Some of them had some really tacky-feeling steering wheels. Although the steering wheel might be tacky due to the steering wheel material itself, in most cases it is simply due to the steering wheel being dirty.