In my last post I said that oni is often translated in English as an ogre, demon or devil. Personally I think that the closest translation is an ogre.
An ogre is a monster that appears in Western legends (伝説) and fairy tales (おとぎ話). It is like a giant, ugly man that likes to eat humans, especially children. Ogres in Western stories are almost always bad, but one exception is the popular character Shrek (though many people in the film think he is bad…).
If we call a person an ogre it means that they are cruel (残虐) or frightening (恐ろしい), like saying「鬼のような人」in Japanese (though we sometimes say it as a joke).
Though an ogre is probably the best word for an oni in a story, the words demon and devil are useful too and can sometimes have the same meaning as oni in other situations.
A demon is usually more like an evil spirit (悪霊、悪魔) and is often connected with religion (宗教) or magic (魔術). The word can also be used for people and sometimes even has a positive meaning, for example “He is a demon cook” (「彼は料理の鬼」).
A devil is also a kind of evil spirit or creature (悪魔、魔王）and is often connected with Christianity (クリスト教) and other religions. The word devil almost always has a negative meaning and is also sometimes used like the word oni in Japanese, for example “work like the devil” (鬼のように働く).
If you can’t find a perfect phrase in English for a Japanese word you can say something like, “It’s like a …” (「…の様なものです」) or “It’s a kind of …” (「…の一種です」). For example if someone asked you, “What is an oni?”, you could say, “It’s like an ogre” or “It’s a kind of monster”.