A STRANGE inversion of expectations marks the ebbing of the hostage crisis. Iran, whose leaders sought to use the situation to unify the nation around the revolutionary leadership, is caught up in internal quarrelsomeness and waves of acrimony over both the seizure of the Americans and the terms of the agreement that set them free. Part of Iran's territory remains occupied, moreover, as the result of a war launched with the sure knowledge that the isolation and disarray produced by the crisis made Iran a relatively easy mark.

Meanwhile, in the United States an episode that could easily have left the country internally bitter and divided has produced instead a rare interlude of shared feelings of unity.Difficult decisions on many issues flowing from the crisis remain to be made. Yesterday, however, this city was awash in appreciation of the valor of the former hostages in the face of their ordeal -- and in a deep satisfaction that just about everyone else shared this sentiment.

It is the former hostages who have set most of the tone of the public observance of their homecoming. No doubt we have not heard all that they have to say. In these first days, however, their courage, dignity, good humor and love of country have come cleanly through. They have evoked some of the qualities that Americans most treasure and that bind Americans most closely. Through all of this, they have been sensitive to the unspoken yet insistent demand that they submit themselves as agents of a kind of national catharsis. Now that they have discharged this extra role, they should be allowed -- by, among others, the media -- to gather up the pieces of their lives in something approaching normal privacy.

"Turn the page," President Reagan advised the hostages yesterday. He could as well have been advising the nation. Certainly he has earned the right: his personal touch had been instrumental not only in helping to bring the hostages home but also in keeping the crisis in perspective. Mr. Reagan resisted making the hostages a cutting political issue during the campaign.He showed graciousness of one sort in sending Jimmy Carter to Germany, and graciousness of another sort in assuring the returneees a family reunion before flying to Washington. He managed with sensitivity and shrewdness to handle a complicated situation that had a large potential for going wrong.He also managed to suggest that a different policy approach will be his in the future, to accept without endorsing the circumstances he inherited -- while promising to move on. It was in that sense, among others, a promising day.