Differences between “en dehors de”, “hors de”, “au-dehors de” and “par-dehors de”?

Question

• en dehors de: outside of, apart from
• hors de: outside the reach of, out of (figuratively)
• au-dehors de: outside of, beyond the border of
• par-dehors de: surrounding the outside of

I'm trying to understand the differences in these prepositions when used in the sense of "outside."

Example:

There is an army outside the city.

• Il y a une armée en dehors de la ville. (outside the city)
• Il y a une armée au-dehors de la ville. (outside the border of the city)
• Il y a une armée hors de la ville. (outside the reach of the city)
• Il y a une armée par-dehors de la ville. (surrounding the outside of the city)

There is not much online explaining these differences. Does this sound right?

Answer 1

Your translations are good.

I'd say "hors de" feels closest to outside, and "en dehors" would be a little bit more like "on the outside" (on the side that is out). But it's just nitpicking.

Most importantly, "au-dehors" and above all "par-dehors" are very old-fashioned.
If I was to utter such a fact, being inside the city, I'd go with:

Il y a une armée dehors.

Also, "en dehors" has a clear opposite, "en dedans", that "hors" doesn't have (so it might be used for contrast if needed).

Answer 2

• dehors : à l'extérieur de ; synonyme de hors
• au-dehors : à l'extérieur ; synonyme : extérieurement, loin
• en dehors : ce qui n'est pas en dedans.