Saturation is really useful. It was a function of tubes and tape back in the day. Since it tends to have a pleasing sound to the human ear, it is used in music to augment the tonal quality of a given sound. It can be used anywhere in the mix. If you look at some of the "VX-64 vocal strip in Cakewalk for example, has input saturation as well as output saturation controls.

As the signal level was increased going into the tape, the tape would reach the point where it could no longer accurately reproduce the signal in a linear manner. This results in what was referred to as saturating the tape with the signal level. It's a form of compression and distortion of the signal. The same thing is true with guitar amps that use tubes. Since tubes and tape are analog, this is a natural occurrence. With digital, not so much. As the signal is increased it simple can't go and the result is an unpleasant sounding distortion. So it was necessary to attempt to recreate the natural smooth compression and distortion found in the analog world and translate that to the digital world.

The distortion from saturation tends to have a "warming" effect on the instruments and vocals it's used on. The key to using it is to avoid overuse just like any other effect. A little bit is perfect but when you put too much in the mix, it can cause other issues. My rule of thumb for using compression and saturation especially, is that if you can "hear it" in the mix, you are using too much.

Even or odd order harmonics. In a nutshell, even order harmonics tend to sound good and odd order harmonics tend to have a hollow or nasal sound that some people don't like. As a guitar player, I have always liked tube amps because they naturally produce even order harmonics in the output stage. Transistor amps generally are the opposite and produce the odd order harmonics. Solid state amps are great if you are playing clean and don't push the amp into the distortion area of it's operational parameters, and, or, you like to use effects pedals. It's a matter of taste and preference. Some of the new digital, solid state modeling amps are really blurring the boundaries between these two worlds. The tone from modeling amps is certainly a force to be reckoned with for guitar tone.

If you don't have it.... A copy of The Studio Engineer's Handbook, latest edition, by Bobby Owsinski is a great investment for your library. He covers everything that you will use in your recording and mixing and explains it in easy to understand ways. There's also an interview section at the back with some rather in-depth insights into 30 or so other top engineers in the recording world that dig into how they do things and why.

You can find my music at:
www.herbhartley.com
Add nothing that adds nothing to the music.
You can make excuses or you can make progress but not both.

The magic you are looking for is in the work you are avoiding.