In Elona, it is possible for either two NPCs, or the player character and an NPC to have sex with one another, regardless of gender (or species, relative sizes of the participants, whether or not they are undead, or even whether or not your character is even an organic life-form with appropriate "equipment" for sex).
Denizens of Tyris are apparently not terribly shy about sex, and will happily engage in sexual activity even out in the streets during any hour of day, even in "respectable" cities. (They also apparently turn a blind eye towards freakish mutant adventurers who keep pet little girls on a leash and will happily buy little girl egg omeletes, so this should probably not come as much surprise at this point...)
For the PC to initiate a sex session with normal NPCs, the target NPC must be drunk. This can be achieved by throwing alcohol on the target NPC (though this is usually considered an hostile action and, probably, a Karma penalty) or waiting for a character to become drunk on its own. Alternatively, giving (by interaction) an NPC an identified, uncursed bottle of alcohol will usually prompt it to immediately become drunk as well. Then, speaking with the NPC will show another option: "Interested in a little tail t'night?"
If your Charisma is high enough, the character and the NPC will exhibit a "heart" balloon (the same shown on an Ally upon killing), and time will go to Auto-Turn mode (as in Rest) with the Log showing flavor dialogue, consisting of the target NPC complimenting your prowess and, apparently, sex sounds. Duration of the act may depend on Charisma. When the event finishes, you will receive gold pieces as compensation, with an amount proportional to your Charisma. You will also receive a bonus in your relationship with the target NPC. As such, prostitution is a good method to achieve money and raise favor with a vendor or adventurer without using love potions, going as far as getting "money back" from the purchase of an expensive deed.
Sex (and its relative abuse) may also lead to several negative effects, including Insanity and sickness. Each act of selling sex will give a -1 penalty to karma, unless you have used the Secret Treasure of the Wicked, in which case there is no penalty. This also trains Charisma for as long as the act continues, being a decent way to train the attribute if you do not have Performer, and have the means to remove any diseases you might contract.
Player characters can also have sex with prostitute NPCs, normally found in Derphy, in which case they are the "buyer" (unless the prostitute is drunk). Such acts do not require alcohol, but cost money, and are almost guaranteed to temporarily dim your character, and carry the same risks of sickness. It does, however, exempt you from the karma penalty. This type of prostitution is beneficial mainly because it raises the player's charisma potential and trains charisma at the same time, but repeated "relaxation" with a prostitute incurrs the same chance to become diseased every time.
Sex also depletes stamina for every round spent engaged in the act (which can last long enough to take up essentially all your sp), so resting four or more times in a row (or sleeping) to regain full stamina may be necessary between bouts.
Prostitution can also occur between two NPCs. Both parties involved in the act won't be available for dialogue, showing the text "is in the middle of something", the same message that appears when an NPC is eating.
In Derphy, sex between NPCs is a common sight. The prostitute NPCs that exist there can randomly engage in prostitution with other NPCs. This still apparently costs money from the NPCs, and if an NPC has no money when they "hire" a prostitute, it can (amusingly) lead to combat between the prostitute and the NPC. (Whom will likely be insane and incapable of effectively defending themselves from the prostitute until it wears off - although high-level characters like Adventurers and trainers will likely brush off attacks long enough to recover their sanity and kill the prostitute.)
If the player owns a pet prostitute (via capturing a prostitute from Derphy), they can randomly engage in sex with other NPCs wherever you take them, and claim money from those characters. This seems to only happen fairly rarely, however. Like with other money that finds its way into the hands of a pet, you cannot directly take this money back, but it can be used to boost the potential of the pet when they are in a town with a trainer. You can also proposition sex with a pet prostitute whenever you wish (provided you have enough stamina) and pay them for it, transferring funds directly from you. Prostitutes can thus fund their own training more easily than other NPCs.