English usage and grammar

Well, there isn't a single usage that's exclusive.

It's a general "oath", akin to any of the less socially acceptable curse words, just not as severe.

You'd use it any time you might be frustrated, angry, or even disappointed. It can freely replace heavier oaths like "fuck me", "fuck my luck", "dammit all to hell", or the ultimate expression of extreme emotion, "mother fucker" (which is distinct in emphasis from motherfucker, believe it or not).

I have seen and heard it used in the older sense, where it represents an expression of sorrow or regret as well, though that is much less common now.

It's my understanding that when it first became used outside of the biblical origin ( John 11:35, when Jesus went and found Lazarus dead in his tomb and cried with those mourning Lazarus), it was used more as a thing where the person would be saying that Jesus would weep with the people undergoing whatever ill event life had thrown at them.

In that sense, it would be akin to saying "alas", or "woe is me".

But, as things often do, it has become more of a complaint against the bad things in life rather than a commiseration with those facing bad things.

It's actually one of the very few bible verses that sticks in my memory, despite some of the mental gymnastics used to explain away the humanity of the story exemplified in the verse. But that's a major tangent.