You would have to search far and wide through the annals of film history to find a more complex, miscreant group of characters than those in “Closer,” an uncommonly engrossing and romantically cynical drama about two men and two women who couple, uncouple and re-couple over the course of four years.

These people are absolute messes, psychologically speaking, which I think is why I enjoy watching them so much — partly in amazement at how self-destructive they are, and partly because their emotions and motivations seem genuinely believable. They’re screwed up, but only in the way that real people are screwed up. Their dialogue is rather theatrical (the film is based on a stage play) and in that sense not 100 percent realistic, but thanks to the almost uniformly excellent performances and direction, the emotions behind the dialogue ring true. You believe the sentiment even when you don’t believe the words used to express it.

The movie is directed by Mike Nichols, whose landmark film “The Graduate” showed that he knew how to use moody pop music to his advantage, and who demonstrates here that he has not lost the knack. The song is “The Blowers Daughter” by Damien Rice, and it plays as the film opens with two strangers walking in slow-motion toward each other on a busy street, catching each other’s eye, a wordless connection being made. That the two people are Jude Law and Natalie Portman tells you that they are beautiful; but Law and Portman also happen to be fantastic actors, capable of drawing an audience’s attention, as they do here, simply by looking at each other. And then, just to make sure you’re really paying attention, one of them is hit by a taxi.

The injuries are minor, but the effect is not: One rushes to the other’s aid and official introductions are made. The next thing we know, Dan and Alice (for those are their names) have been together a year, sharing a flat in London, where Dan is an obituary writer with a novel in the works and Alice is, in her own words, “on an expedition,” doing the sort of European wandering that many American youths do (at least in the movies).

Their relationship is threatened by Dan’s sudden interest in Anna (Julia Roberts), a photographer whom he meets in the course of his work. Alice knows Dan has hit on Anna and is hurt by it. To her credit, Anna refuses his advances, and Dan retaliates by attempting to embarrass her in an online chat. This childish prank leads to her meeting a new man, a doctor named Larry (Clive Owen). They fall in love.

These two couples have met, as you can see, under unusual circumstances, and their relationships persist only tenuously. I get the feeling sometimes they stay together only because they have such great “how we met” stories, and breaking up would ruin them. Certainly at least three of the four are particularly interested in monogamy, for soon the couples have mixed and matched in various ways with various dramatic consequences.

I have always believed that the one thing everyone in the world wants is to be happy, and that life is simply the ongoing attempt to figure out what will achieve that for them. The characters in this movie aren’t even close to figuring it out. The one thing they know, if they search themselves carefully — which they do not — is that they don’t know what they want. When Larry complains about his and Anna’s apartment’s bathroom, she says, “You chose it.” His reply: “That doesn’t mean I like it.”

The one character among the four who exhibits signs of emotional stability is, ironically, the one you’d least expect it from: Alice. Played by Natalie Portman with astonishing conviction, poignancy and range, Alice’s response when faced with emotional abandonment by Dan is to put up her figurative armor by taking off her literal clothes: She goes back to work as a stripper, a job she had in New York before sojourning to England. A scene set at her workplace between her and Larry is fraught with anger and sexual tension, a marvelous moment from Clive Owen and one of Portman’s several brilliant scenes.

The weak link in the cast is Julia Roberts, whose performance is merely OK while the others’ are superb. She is too glossy to be a complex, dichotomous woman like Anna; her “Erin Brockovich” Oscar notwithstanding, Julia Roberts simply doesn’t have the depth to pull off something this complicated.

For as much sex as there is in these characters’ minds and dialogue, there is no sex in the film. It all occurs offscreen, Nichols and Marber having realized that sex itself is not a very interesting thing for a movie to focus on. It’s the aftermath and the beforemath (if that were a word) of sex that make for rich character drama.

A- (1 hr., 43 min.; R, abundant filthy language and bawdy talk, a little nudity.)