A citrus-based degreaser is wonderful for many purposes, cleaning up much of the slaughter and leaving a nice citrus smell in its path. (This is useful to keep pet helpers out of your kitchen as you clean.) Many of these can get rid of things like tar stains and lipstick, so an oil slick from that dropped hamburger patty should be no match. If we're talking a whole greasy pan of burgers you'll need a bigger gun.
For an environment like a busy restaurant kitchen, a commercial grade multi-purpose cleaner is your best friend. These can remove grease as well as wax and are geared for commercial situations. Many of these are suitable for food processing equipment and stainless steel.
For those who are chemically sensitive, there are butyl-free and fume-free degreasers too.
When you're dealing with greasy floors, you need a good neutral detergent that will remove the grease but not damage your floor finish. Something like this can be used to clean the walls too, so it's economical and it's not limited to just slick floors. This is great for backsplashes, since they are probably christened from frying pans and woks slung around in a popular joint.
Machine oils are a whole other obstacle. Industrial settings need something more powerful like a heavy-duty degreaser that gets oils off factory walls and light machinery. These break the grease down so it can be sluiced away with water. These are strong and to be used with caution around more fragile surfaces, but they go through grease like, well, like a hot knife through butter.
We Fight Dirty!™ . . . and we don't leave anything behind.