I have been watching this thread, but I have been too busy to jump in.
Few points:
First, all the talk about flux is scary. There is flux and there is flux.
I use very good quality rosin core solder. There is separate rosin flux available, but if you just go into a hardware store for flux, odds are you will get one of the various acid fluxes designed for plumbing.
Since I do lot electronics work, I am especially sensitive to the danger of acid flux. If you use it on automotive connections, the resulting corrosion will destroy the connection you made, and ruin a section of the wires involved. But if you cut away enough of the wire, the car can be saved.
If you use it on a circuit board, almost certainly the entire board will be destroyed, plus any other boards soldered with that same soldering iron tip will be damaged.
I have been called in too many times to try to save equipment that was damaged that way. I never have enjoyed standing in a manager's office holding a $5,000 circuit board with a small green spot on it and telling him its not savable.
Next, I'll get some flack about this, but a properly crimped joint is superior to a soldered joint every time. And I do not say that lightly. Remember I make a living soldering and I am very good at it.
The key is the properly crimped part. Plus the connector has to be good quality. There was a big study done many years ago about crimped joints, but I can't find it right now.
The reason crimped is better, has to do with the nature of metal. When you look at a piece of nice clean shiny copper wire, you are not actually looking at the real metal.
You are looking at a tiny layer of oxidation on the outside of the metal. Most all metals form an oxide layer within seconds of being exposed to air.
In theory, you could tear a piece of metal in a vacuum, press the edges back together and it would reform back into the original piece.This doesn't happen because the molecules in the edges spring back and recombine with others to change the shape of the tear. But the edges will stick to a certain extent.
And in fact, there is a phenomenon known as vacuum welding which takes place in space and must be allowed for when designing spacecraft.
The oxides will boil off the surface of a metal, and if those ultra clean surfaces touch, you will get micro-welding occurring without any outside heat.
In a proper crimp, the two surfaces of the metal, the wire and the connector, are pressed together so hard that the outer layer of each will be displaced by the other resulting in truly clean metal touching under high pressure.
This forms an almost perfect joint that is not only waterproof, but is actually gas tight. In other words, no oxygen can get in to corrode it, and for all intents and purposes, its all one piece of metal.
Basically a cold weld.
Plus, a solder joint, particularly in stranded wire, will cause a stress riser where the solder ends because the solder causes the stranded wire to be rigid where the solder. But it is still flexible where it is not. So all the flex occurs at the edge of the solder.
You will notice that all the connectors built into those relays are all crimped onto the wires. There are two reasons for that. One, its cheaper to have automatic equipment crimp the wires than pay someone to solder them, plus the crimped joints are the best way to go.
But, everybody here has stories about crimped connectors they have used failing after a while. That is because a properly crimped joint is difficult.
It requires both a fairly expensive ratcheting crimper, with the correct jaws for that connector, and good quality connectors with the right hardness metal.
Too hard a crimp or too soft a crimp, and you have a bad connection.
Also, I really don't like those connectors at that Amazon link. I use some like those, but mine are the crimp type. You put the wires in, touching the solder ring in the center.
Then you crimp the wires between the solder and the outside with a good crimper.
Then, when you heat the joint, the solder melts enhancing the joint, but not wicking to any moving wire. Then the adhesive lined heat shrink melts and shrinks sealing the whole thing.
They look a lot like those, but they are crimpable which those are not.
As to the original question, when attaching multiple wires to one terminal, it depends on the size and number of the wires. Two small wires can often be crimped into one connector, but if not, then I often join the wires together away from the connector with a butt splice and have one wire coming out the other end which I then crimp to the terminal connector.