Eunuchmeans castrated male, to put it simply, it refers to a man with his penis removed who guarded a harem. At times, children were also made eunuchs in childhood to sing soprano in church choirs.
Euphemism refer to language that substitutes a word or expression that is thought to be less distasteful or offensive for one more exactly descriptive of what is intended.
Euthanasia refers to an act or practice of causing death painlessly in order to end suffering: advocated by some as a way to deal with persons dying of incurable, painful diseases.