• 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.

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).