The Banshee is always found in a room in the center of the level.
Alternatively, a male character can wield a wedding ring. In this case the PC in question still hears the Banshee's wail, but it does not damage the PC. The Banshee is still hostile, however. The Banshee's wail is displayed to a male PC wielding a wedding ring as follows by the game:
The banshee regards you in astonishment. "My beloooovvveed huuuusbaaaaaaaaaaannnd!"
Beware of trying to lead the Banshee around while wielding a wedding ring. While her wail can be exploited (see below), this is a dangerous practice. The wedding ring only works while the Banshee can see the PC, so leaving her line of sight for even a single turn can be fatal.
The Banshee routinely shrugs off bolt spells, but can eventually be killed using them. She is not difficult to kill in melee.
Players have exploited the properties of the Banshee by having her follow a deaf PC around. Her wail kills many monsters. A report from the Russian ADOM newsgroup (January 16th, 2001) reveals that the trees in the animated forest are vulnerable to the Banshee's wail. As might be imagined, dozens of trees dying every few turns leads to some very nice treasure. The downside is that the Banshee will become very experienced very quickly, thus making her much more difficult to dispatch should the need arise. NPCs known to be immune to her wail include Waldenbrook, Thrundarr, the Eternal Guardian and the Casino shopkeeper. Banshees can be wished for. There have been reports of wished-for Banshees being effective against some of the monsters found on D: 50 in gamma 12, but most seem to be immune in later gammas.
A blessed stethoscope is not helpful as far as the Banshee is concerned. The game states the Banshee appears to be rather dead. The monster memory contains the following after killing the Banshee:
<<<<<--- Banshees (G) --->>>>> The banshee, a luminous spirit, manages to appear sad and angry at the same time, obviously a being in an enraged lamentation. Her wail is renowned as it is filled with such sorrow and hopelessness that most who hear it abandon life instantly, passing beyond their current pains. Banshees seem to have a DV of 40. They have a PV of about 2. They seem to have 187 hitpoints on the average. Usually they attack 2 times. They seem to have an average speed of about 107. So far you have killed but one banshee. One kill on the average seems to be worth 61779 experience points.