Without their big daily newspapers for a full week now, New Yorkers, who like to boast that they live in the nation's media capital, are facing an unlikely assortment of make-do substitutes, including one tabloid whose reporters are working out of an apartment house storage room.

"There's no question this is a break for us, but publishing a big-time city paper is really not my thing," conceded Edward Kayatt, whose thriceweekly tabloid Our Town is put out by a handful of reporters working in a basement room that until recently was full of tricycles and baby carriages.

Until employes at The New York Times, Post and Daily News shut down their papers last Wednesday in sympathy with a strike by the 1,600-member printing Pressmen's union, Our Town's circulation was confined mainly to giveaway copies left in apartment lobbies.

As one of the few local papers remaining here, however, Our Town has doubled its press run to nearly a quarter million. The newspaper has moved onto the newsstands here and now costs a quarter a copy.

"I don't know how much money we'll make, but I hope this brings us some respectability after all this is over," Kayatt said yesterday.

It won't be long, though, before his paper is joined by a small host of quickly assembled new dailies, whose staffs are mostly composed of out-of-work members of the big papers and whose owners in some cases have been waiting for years for a clean shot at the big New York newspaper market.

"They'er coming out of the woodwork," said Charles Hagedorn. "Once that clique of big owners breaks, everybody wants to get in and get his chance," said Hagedorn, who publishes six small weekly papers here. Tomorrow his Hagedorn Communications Inc. is to begin City News, the first of the markeshift dailies to hit the streets of New York.

Hagedorn's paper will have 30 to 40 from The Times, Post and News, and reporters and editiors siphoned off will sell for a quater. He estimated that the initial press run will go to about 250,000 copies of a 56-page tabloid.

Hagedorn published his last interim paper 15 years ago, when New York's daily newspapers were struck for 114 days.

I was born and raised in New York," said hagedorn's son, Christopher, who will help publish City News. "I get confused when I open my apartment door during the strike and see the Philadelphia Inquirer lying there."

The City News publishers said they had no illusions about making their pickup paper permanent. "The day the newspapers come back is the day I go out of business," said the younger Hagedorn.

Ralph Clifford, another aspiring daily publisher, said he plans to get his strike paper, The New York Graphic, into print within a week with an initial 50,000-copy press run. "It's going to be an all-day newspaper," said Clifford, a former reporter for the old Brookland Eagle.

So far, however, Clifford has only four reporters and a logo from one of New York's lively 1920s tabloids that he registered for himself after the 1963 strike. He said he plans to put out the paper from the tiny downtown newsroom that houses employes of his six weekly papers.

The publishers said they had heard of at least a half dozen other plans to start papers, and several syndicates have been busy in the last few days here searching the city for financial backing.

Meanwhile, out-of-town papers, including The Washington Post, The Boston Globe, The Philadelphia Inquirer and Newsday have all increased their newsstand circulation here in anticipation of a long strike.

The New World, started in December 1976 by followers of the Rev. Sun Myung Moon, has upped its circulation from 51,000 to 300,000 here since the strike began. "Our phones have been ringing off the wall," said the paper's advertising director, Ashly Nobel. "We even had to hire two out-of-work people from The New York Times to help us take ads," he said.