What would be the best option for protecting the inhabitants of a
tidally-locked world from the weather?
First, what's the problem with a tidally-locked world? Basically, one side of the planet will always face the system's star. That side would get very hot. The opposite side, being locked in a position of permanent night, is very cold.
Let's not worry about how hot or how cold it is on the respective sides for the moment. The important point is that one of the basic laws of thermodynamics says, I'm paraphrasing here, that heat travels from hot zones to cooler zones. This will happen by whatever conductor(s) is(are) on hand. In this case, the atmosphere will do a great deal of work here. That makes wind. Generally speaking, the hotter the light side is in relation to the dark side, the stronger the wind will be.
So, if you want to kill off those winds or at least slow them down on a planetary level, you have to do something about that temperature differential. If you have technology to terraform the planet then you could also, while you're at it, add a Solar Shield and a Solar Mirror to the mix. I would argue that it may even be easier to do that than try to build reliable protection from the winds on a settlement by settlement basis.
In this case, the Solar Shield I envision is a circular mesh deployed at the L1 point. It would not stop all the light but it would block a percentage of it. The shade lowers the temperature on the light side. Also, a mirror deployed at the L2 point could reflect some light to the dark side. If the makers are smart about it, they would make these two objects complement each other. In other words, the heat energy blocked by the shield on the light side would equal the amount of heat delivered using the mirror on the dark side. Indeed, a step more along that line of reasoning would allow the devices a limited amount of "intelligence" and the ability to give the tidally-locked world real day/night cycles.
So, the version 2 shield is not a mesh but a material that has two states, fully opaque or partly opaque. The control mechanism being how much of an electric current is running through it. This is similar to composite materials used today in high-tech windows of tomorrow. Version 2 of the mirror would likewise be covered with the same material but with a range of fully opaque to clear. That would allow the mirror to go dark as needed. With both devices in place, the light side could experience night while the dark side got day.
Regardless of which versions you use, the end result is to bring the world's areas of extreme down to a more moderate level. That would help with the wind problem. With these great extremes the heat exchange, which is the source of the massive winds, becomes more moderate. That makes the winds more moderate.
Now, I'd like to point out that success here may not cause the wind to cease completely. It is more likely to bring the winds down to a more manageable level. A level that would allow the individual settlements, at a much lower tech level, to build things that could survive the wind.