Well I'm only interested in character's walking, nothing mouse related.
Moving is mouse related, you change direction by mouse (most of pc users anyway use a mouse and kb type setup for pc), or similar controller.
It should affect all characters in the world, including animals and such.
No, I don't have a method for it to affect all characters, and a script running for every active ref is unrealistic.
I was hoping someone experienced could do it since I have no experience with the engine,
Yes, that is why I explained what *I* could do and refereed to the personal pronoun in my post. However there are definitely peeps more experienced in the forum and some may have a more elegant solution. However you still have to work within the boundaries of what's possible with the game.
even the notion that I have to use a quest to add such effects is weird to begin with xD
Standard operating procedure, you'll see it over and over again. Scripting is what gives fallout it's flexibility to do so many things, and quest scripts are often used to implement them.