In your example sentence "to be hanged" is the infinitive of the passive form of the verb "to hang":
In the morning, the hangman will hang the narrator.
In the morning, the narrator will be hanged (by the hangman).
The people hastened from the town to see the hangman hang him (the narrator).
The people hastened from the town to see him (the narrator) be hanged.
In your example sentence, "to see him hanged" describes the reason why the townspeople are "hastening out of the town" and is essentially timeless. From the perspective of the townspeople, the hanging is in the future, but the entire event could take place in the past, present or future, depending on the rest of the context:
(past) The townspeople streamed from the town to see the man hanged.
(present) The townspeople are streaming from the town to see ...
(future) The townspeople will stream from the town to see ...
If you want to emphasize that the hanging is in the relative future (and therefore still uncertain), you can say something like:
... to see the men who were to be hanged.
If instead you want to say that the townspeople are coming out to see his body after he had been hanged, that's how you would phrase it:
The people streamed from the town to see the men who had been hanged.
Side note: Past participles can also act as adjectives, in this case modifying the narrator who, in the near future, will be a hanged man.
Adjectives by themselves are timeless, so you have to rely on the context to determine the time frame. However, "hanged", like "finished" or "awakened", is a binary state -- which is to say, you can either be hanged or not hanged, but you can't be somewhere in-between. For this reason it's possible to use a participle to write a sentence with your meaning 1:
The cowboy rode silently past the hanged men, away from the town and out into the desert.
or meaning 3:
The cowboy rode silently past the sullen group, who knew that, the next morning, they would all be hanged men.
but not meaning 2. If you want to write about a hanging in progress, use the present progressive:
"Look, they are hanging the men now!" the children called out, as the cowboy rode away from the town and out into the desert.
