What was going on when I was born?

New Yorkers On New York Third article of a series appearing periodically. By KENNETH A. BRIGGS New York City residents - rich and poor, black and white - go to churches and synagogues about as often their counterparts across the country, and many say that personal prayer is a fixture in their lives. While the religious mix of New Yorkers differs from the national profile, 4 in 10 city residents interviewed in a new survey by The New York Times said they had attended their church or synagogue in the previous week, and more than half reported that they prayed daily. The level of church attendance matches other sections of the United States and runs counter to the general impression that many residents of other states have of New Yorkers.

The Polish Ambassador to Japan has defected to the United States to protest the military crackdown in his homeland, American and Japanese officials announced yesterday. The 51-year-old Ambassador, Zdzislaw Rurarz, defected on Wednesday and flew with his family to the United States yesterday. He said he could no longer represent a ''regime which denies the fundamental rights of the Polish people.'' Mr. Rurarz was the second Polish envoy to be granted political ayslum in the United States this week. Warsaw's Ambassador to Washington, Romuald Spasowski, defected Sunday, also to protest the military takeover in Poland.

President Reagan has come to the end of a year of dramatic political change facing serious potential problems, but many politicians and voters say the difficulties do not yet appear to be punishing him or his party. The strength of his position, and thus his opportunity to influence voting in 1982, comes through in interviews with politicians and voters, poll takers and small-business men around the country. From unemployment to budget deficits, from what some perceive as unfairness to the poor to growing antagonism from women and blacks, Mr. Reagan and the Republican Party almost appear to have stockpiled future troubles, some of them self-inflicted. Yet, according to the interviews, the President generally remains politically above the troubles and appears to be keeping his party buoyant as it approaches what may be the most important off-year election since 1934. Agreement on Budget Cuts Robert M. Teeter, president of Market Opinion Research in Detroit, said, ''People really agree with him that cutting the Federal budget is very important.''

Secretary of State Alexander M. Haig Jr. said today that it was ''very important'' for the Western allies to follow the lead of President Reagan and ''apply whatever pressures'' they could to bring about an end to the repression in Poland. Amplifying on Mr. Reagan's address Wednesday night, which outlined economic sanctions against the Polish Government and included a warning to the Soviet Union, Mr. Haig said the crackdown in Poland had made it difficult for the military Government to allow a return to the liberalizing situation that existed in Poland before the imposition of martial law on Dec. 13. That is why, he said, ''it is very important that we do what we can, not only in the United States, but together with the Western world, to apply whatever pressures we can to reinstitute moderation and continue the process.'' No Allied Consensus Mr. Reagan, in his address Wednesday, said the United States would discuss with its allies joint action to deprive Poland of hightechnology imports, but he did not call on them to participate in any coordinated program against Poland or the Soviet Union.

A ruling by a Federal judge yesterday would permit the United States Steel Corporation to purchase the Marathon Oil Company for $6.3 billion on Jan. 7, thus ending a two-month takeover battle with the Mobil Corporation. Mobil's competing offer of $6.5 billion remained bogged down in court rulings that the nation's second-largest oil company would violate antitrust laws if it bought Marathon, which is the 17thlargest oil company. There seemed little chance that it could win a reversal of these rulings before U.S. Steel is freed to purchase control of Marathon in two weeks. In yesterday's ruling, Judge Joseph P. Kinneary of the Federal District Court in Columbus, Ohio, said that Marathon stockholders had until midnight Wednesday, Jan. 6, to take back their shares tendered to United States Steel.

New York State's prison system was legally restrained today from double-bunking - the practice of placing two prisoners in a cell -and from using prison corridors, recreation areas or dormitories to confine inmates. The order, by a State Supreme Court justice in Albany, appeared to put the state's Commissioner of Correctional Services, Thomas A. Coughlin 3d, in a peculiar position. Just two days ago, a Federal judge in Manhattan ruled that the state's prisons, which are now 12 percent over capacity, must speed the transfer of state prisoners held in New York City jails. Mr. Coughlin said Wednesday that he would refuse to comply with the Federal order, which he contended would force him to create unsafe conditions.

In Bethlehem, Msgr. Giacomo Beltritti, flanked by Mayor Elias Freij and Lieut. Col. Shalom Noni, Israeli military governor, on the way to Christmas services at St. Catherine's Church.

Gen. Wojciech Jaruzelski, the Polish leader, declared in an address to the nation today that there was still a place for independent labor unions in Poland. He also denied that hundreds of Poles had been killed or held in inhumane conditions since the imposition of martial law. General Jaruzelski, the Prime Minister and Communist Party leader, said he could not wish Poles ''a merry and prosperous Christmas.'' He said he realized ''how the rigors of martial law have complicated everyday life and thwarted personal plans.''

Delta Air Lines yesterday announced price cuts of up to 51 percent on its normal coach fares between 24 Northern and Middle Western cities and its nine Florida destinations, including a $114 fare between New York and Florida. The new fares are effective Jan. 6. The move, which could set off another fare war in the New York-to-Florida market, was seen by industry analysts as a bid by Delta to protect itself from competitors' inroads into its markets and to stimulate Florida traffic, which has been hurt by the slowing economy. Poor Showing in Reservations Although Delta did not give full detail on specific fares, Gregory Hughes, in charge of public relations for Delta in the New York area, said that its regular coach fare from New York to Florida cities would drop from the present $159 one-way to $114 on weekdays. Higher fares would apply on weekends, but Delta did not give a precise figure.

Fifty-two leaders of Turkey's Confederation of Revolutionary Trade Unions were put on trial in Istanbul today with the prosecution asking for the death penalty. This is the first time since the armed forces took power on Sept. 12, 1980, that a military court has demanded capital punishment for suspects not directly linked to terrorist activities. One of the two major labor unions in Turkey, the Confederation of Revolutionary Trade Unions was immediately suspended when the Turkish Army ousted Suleyman Demirel's elected Government. More that 350 of its members and leaders were detained, and later 52 of them were formally arrested and remained in jail.

Cardinal Tomas O Fiaich, the Roman Catholic Primate of All Ireland, issued a call for unity today and appealed for a Christmas cease-fire in Northern Ireland's sectarian bloodshed. The holiday period should be a time of ''joy, love and peace for everyone,'' he said, adding, ''I hope the only guns displayed over Christmas will be in the holsters of cowboy suits.''

Four American veterans of the Vietnam War left here today after a six-day visit, convinced that they had achieved a breakthrough with the Hanoi Government and nervous about the reception that awaited them at home. ''We've got to be very, very careful,'' said Michael Harbert, a New York management consultant who is associate director of the Vietnam Veterans of America. ''This is only the start. We can't go back to the United States and say that Vietnam is a great place because we accomplished a great deal. Vietnam is not a great place.''