I am a little confused with them because sometimes they have been translated similarly...
In fact the words are very similar, and they even form a circular definition in the dictionary. From NOAD:
a feeling of discontented or resentful longing aroused by someone else's possessions, qualities, or luck
jealousy (n.) the state or feeling of being jealous
jealousy (adj.) feeling or showing envy of someone or their achievements and advantages
As to how they are used in everyday conversation, I'd say that jealous can cover a wide range of emotions, from the angry, resentful rage of a jilted lover, to the playful admiration of a friend.
Of the two words, envy is seldom used in the context of spurned lovers or unrequited love, while jealous is often used in that context:
"...he must have transferred part of his love to other women or to another woman — and she was jealous. She was jealous not of any particular woman but of the decrease of his love." (Tolstoy, Anna Karenina)
Yet the word jealous is sometimes used to express much more mild forms of envy as well:
Beth: "My parents are taking me to Europe next summer."
Seth: "I'm so jealous!"
Without any further context indicating the contrary, I'd guess that Seth is not expressing any simmering resentment; instead, he's using the word jealous in an informal sense, and admiring Beth's good luck in a friendly way. In that context, "I'm so jealous!" simply means: "I wish I could go to Europe, too!" But a deeper and more negative form of jealousy would mean: "I wish I could go to Europe, instead of you!"
As for your three examples, I'd go so far as to say that jealousy would probably be the more appropriate word for scenario #2 (the love triangle), but either word could be used for the other scenarios, and choosing the better word would depend on two factors: the depth of negative emotion felt by the person exhibiting the envy or jealousy, and what that person happened to be envious or jealous about.
Both words are considered generally negative, particularly when the feelings linger for long periods of time. Without any further context, I'd say that envy is probably a milder form of covetousness than jealousy. For example, if I heard either of these two sentences:
I am envious of my neighbor's new car.
I am jealous of my neighbor's new car.
either of them could mean nothing more than the person saying it's a very nice car, but I'd say the latter runs a higher risk of being interpreted as a negative and highly self-centered remark, to the point where the speaker is begrudging the neighbors for their new wheels.