The situation between the United States and Iran is rife with anamolies, one being James Abourezk, the jolly former senator from South Dakota. Abourezk's law firm represents the Khomeini government in its suit to recover $56 billion from the ailing shah and his wife.

Before your eyes cross in anger, remember that Hodding Carter, the State Department spokesman, sometime ago publicly urged the Islamic Republic of Iran to use legal means to redress its grievances, such as its claim on the shah's fortune, rather than resorting to illegal means, such as holding Americans hostage.

So what Abourezk has been doing for eight months -- serving as Iran's lawyer in the United States -- is within State Department guidelines. The Abourezk firm filed suit in New York state court on behalf of the Iranian government, charging that the shah diverted $10 billion in government funds to his personal use and asking $30 billion more in damages for other alleged abuses of Iranian funds.

Another familiar liberal, Democratic name, Paul O'Dwyer, is involved in the Iranian government suit against the shah. O'Dwyer is counsel in New York for the suit. He is a former New York City Council president, an unsuccessful candidate for mayor, and brother to the late Bill O'Dwyer who was mayor.

Abourezk returned from Tehran last week, but won't talk about how he does his business with high-ranking officials of the Khomeini government. He doesn't think that public statements by him will help anyone involved in the case, and certainly won't help the American hostages.

There's good reason to believe that Abourezk, when he sees an Iranian official like Foreign Minister Sadegh Ghotbzadeh, as he does regularly, uses a form of quiet diplomacy to reduce the hostile attitude toward the United States -- hoping that this approach might aid in the release of the hostages.

Abourezk had a fast, eight-year career in the U.S. House and Senate and won a quick reputation as an outspoken liberal whose feisty views did not recommend him to be ambassador to anywhere. But he's an authentic, good-natured fellow, who can easily pull off his necktie and strum his guitar; thus he was always popular in Washington. His supporters were sorely disappointed when he decided to quit the Senate after only one term. Abourezk, a Lebanese-American, also became a strong critic of U.S. Middle East policy, claiming that it was unfairly tilted on the side of Israel over the Arabs.

He says that he never sought the Iranians as clients; rather, it was Shahriar Rouhani, then the ayatollah's liaison man in the Iranian Embassy here, who came last spring, asking him to handle the revolutionary government's legal affairs in the United States. The ayatollah bunch couldn't fathom how the American court system operated, the argument went, so Abourezk took them on as clients.

He did not advertise his relationship with the Iranians and is grateful that it is so little known, that angry and/or obscene phone calls have been minimal -- even through the hostage-crisis period. Abourezk has made several trips to Tehran this year -- two within the past month -- and apparently is on good terms with the ayatollah's regime.

The United States and Iran still have diplomatic relations, though official communications seem nil. Most of the communicating is by means of the American media, which the revolutionary government accommodates grandly and therefore exploits. The Iranian Embassy here freely grants visas and press credentials to American journalists so they can hurry to Tehran for the Big Story. Visas are issued to other persons, but in fewer numbers. Pan-Am canceled its thrice-weekly New York to Tehran service in early November, shortly after the Americans were taken hostage, but other international carriers maintain schedules to Tehran from Europe.

Meanwhile, the Abourezk firm is quite busy trying to sort out Iranian claims on holdings here that one partner, Thomas Shack, estimates involve "hundreds of millions of dollars, perhaps billions." The U.S. government has frozen Iranian government assets in the United States but not private holdings. Shack argues that since Iran can't use its money tied up here by the freeze, American vendors are being denied payments due them.

There seem to be bushel baskets full of litigation for the firm these days. Abourezk says that his Iranian government client will also file suits against the shah in Geneva and that his firm has assigned Iranian cases to local counsel in New York, Chicago, San Francisco, Boston, Dallas and Houston.

Sometimes I think if the Americans and the Soviets or anybody else got into war with each other, the lawyers in the warring nations would continue doing business. As for all those billions the shah is supposed to have squirreled away, why, everybody knows they are in Henry Kissinger's basement. s