At Sacred Heart Parish, 16th and Park Road NW, the number of families receiving church emergency food packages jumped from 70 last July to 230 in May of this year, according to the Rev. Joaquin Bazan, pastor.

SOME (So Others May Eat), a church-operated soup kitchen half a mile north of the Capitol, has watched its daily line grow from 200 persons a few years ago to 600 today.

In affluent Montgomery County, $30 emergency aid grants given by the interdenominational Community Ministry jumped from 16 a month three years ago to over 100 in June of this year.

"I don't know where it's going to end," says Marita Dean of Catholic Charities' crisis intervention service. "Last summer we were seeing 40 people a month. Now, it's close to 100. And this is summer, when it should be down. God knows what it will be in November and December."

"The churches I know are overwhelmed by the tide of need," says the Rev. Jack Woodard of St. Stephen and the Incarnation, a Northwest Washington parish where he reports the number coming for emergency groceries has tripled since last year.

Nearly a score of other Washington area agencies, the heart and soul of President Reagan's hopes for voluntarism, report they are being strained beyond their capacity to cope.

They have watered the charity soup, giving less help to more people, to stretch their resources. They have redoubled efforts to raise additional funds and supplies, in some cases scavenging food from supermarket dumpsters -- but they say the same problems of inflation and unemployment that multiply the appeals for help are cutting deeply into contributions and operating revenues.

And so, increasingly, they have had to steel themselves to sending people away empty-handed.

"We tend to run out," says Noreen Buckley who runs the food pantry at St. Stephen's.

"We help what we can and after that we have to say, 'Sorry.' We have to turn people away."

At the same time, they are also turning to political pressure in their effort to cope, taking every opportunity -- through testimony at legislative hearings, through pronouncements, through lobbying -- to demand a reversal of cuts in government welfare programs.

"We do not need to be reminded of our responsibilities to the poor," said Roman Catholic Archbishop James A. Hickey earlier this year, responding to Reagan's suggestion that the churches take over more of the welfare burden from government. " . . . Our efforts cannot and should not substitute for a national commitment to build a just society . . . "

The Rev. Tom Nees, Church of the Nazarene minister, who heads a congregation along the 14th Street corridor, says, " . . . The first responsibility of the churches is to create that moral climate in which it is politically unthinkable to do what is going on in this town . . . . "

Officials say church involvement in charity work is already so extensive that it is impossible to estimate the total amount of aid provided by area religious groups.

In Washington alone, religious institutions operate nearly 60 food pantries or soup kitchens and 14 shelters for the homeless, where some food also is available.

SOME by itself estimates that its food and volunteer labor are worth more than $1 million annually.

In addition, religious institutions provide some free or limited-cost care at affiliated hospitals, aid for utility and mortgage or rental payments, counseling -- the list of their services touches all the needs of man.

Church aid programs traditionally have been an emergency backup system for government-funded assistance programs. In recent months, the federal welfare cutbacks plus the effects of inflation and rising unemployment have produced more emergencies than the churches can deal with.

"Anybody who is single and who does not have family support is just one RIF away from disaster," says the Rev. Jennie Bull, minister of outreach for the Metropolitan Community Church.

The result is that church charities now are getting pleas for the kind of help that is far beyond their resources.

There are, for instance, what Tina Sturdevant of Catholic Charities of Prince George's County calls "a new class of poor." They are the couples with young children, a house and a mortgage based on two incomes. They are proud of their achievements. Then one of them loses a job. The family still has an income, but it's not sufficient to pay the high mortgage payments and utilities.

"These people put every cent into the mortgage -- money that should have gone into medicine for children, into shoes for the children. So these people are losing their home when they come to us."

She recalls the anguish of the young mother who had to give away her children's dog because they could no longer feed it, and she adds softly, "I have seen men cry in my office because they lost their job and can't pay the mortgage."

There is little Catholic Charities can do to help. Sometimes, she says, "we help them" with a food package or used clothing "so every cent can go toward that mortgage, so maybe the one who lost the job can find another. But if the amount is way too large, there's not much we can do."

Others come with huge, long-overdue utility and rent bills. "We've had families who have had to make a choice," says Catholic Charities' Dean.

"They can't pay the oil bill" during the cold weather, "so they use electricity to heat. Then comes spring and their electricity is turned off" for non-payment.

"We negotiate with the utilities . . . Maybe they owe $200-$300. We call and send in whatever they'll accept to keep the service continued. For some . . . once it's cut off they'll never be able to get it re-installed" because of the backlog of unpaid bills.

Unpaid rent is a similar problem. "Somebody who is back in the rent two months -- you're talking about $800-$900," Dean says. "There's no way we can pay that amount."

In such situations, says Delores Farrow of the Righteous Branch Commandment Church of God, church charities "bag around," searching out other religious groups, local churches, possible government sources and family or friends who might chip in so that together the total amount is raised.

This tends to be a one-time-only solution, Dean says. "If there isn't any money coming in, what are they going to do next month?"

In such cases, she says in a troubled voice, the appeal has to be turned down. "It's a hard thing to do, 'cause what is there but the shelters? It's not an easy thing to . . . ." She does not finish the sentence.

In the inner city, where the need is most acute and the resources most limited, religious groups rely on a variety of devices. Most have developed support systems linked to churches and synagogues in the suburbs or more affluent sections of the city for contributions of foodstuffs, volunteers, and cash.

SOME, for example, has a network of 70 churches and synagogues that take turns providing and serving 600 breakfasts and lunches, from the exotic spiced and fruited oatmeal of the Sikh Dharmas to the monthly soul food lunch from Shiloh Baptist.

Most food pantries and soup kitchens get some food from the Capital Area Community Food Bank, where commercial food processers and handlers can receive tax benefits for donating food that is still edible but outdated, damaged or otherwise unsalable.

The problem with the Food Bank, charity workers agree, is that by its very nature, its inventory sometimes tends toward the exotic and lacks the essentials.

"It's not the choice of foods you can keep a family going on, even for a day or two, and that's all we're trying to do," says Sister Julia McMurrough of Assumption Church in Anacostia.

Like most emergency food program operators, she must buy supplementary food supplies, especially protein items, to supplement the Food Bank's stale English muffins and packets of holiday colored M&Ms.

Conversations with church social service workers reflect a scrabbling for resources, wherever they can be found.

Some groups scavenge still-edible food from dumpsters outside shipping terminals and supermarkets and make regular rounds of restaurants and hotels to pick up left-overs.

"We get buckets of beautiful food -- not off people's plates but food that hasn't been served -- from dinners at the Organization of American States," says the Rev. Dr. John Steinbruck of Luther Place Church in the District of Columbia.

Church welfare workers, trying to raise funds, spend a lot of evenings telling church and community groups about the problems they wrestle with during the day, in an effort to raise funds. "The personal touch helps," says Sturdevant.

While excess zucchini from summer gardens in Potomac often nourishes soup kitchen patrons in Columbia Heights, contributions of cold cash are harder to raise.

The Community Ministry of Montgomery Country, which has watched its Grant Assistance Program expenditures rise from $6,872 in 1979 to $15,115 last year, is pressing the more than a score of church groups that support it for $20,000 to meet this year's needs.

Given the current economic situation, fundraising is not an easy task. "We're just about holding our head above water," says the Rev. T.J. Baltimore of the People's Community Baptist Church in Wheaton. His congregation of black middle-class professionals and government workers falls in the $25,000-a-year class, he said.

"My counseling load has doubled," he says. "I get 20, 30 calls a day . . . all hours of the day and night," as both members and people from the community turn to him for help.

"Poor folks are looking to us" for help, he says, "but I'm having real trouble finding the money, finding clothes" and other items they need.

In Alexandria, Rabbi Sheldon Elster of Agudas Achim Congregation, reports similar problems.

"There are a lot of people" within the relatively comfortable congregation "who really need assistance," he says, adding that the treasurer of Agudas Achim has had "a constant load of people who need adjustments" in their membership fees as family incomes fluctuate.

Throughout the area, charity workers say they are fearful for what the future holds. At St. Stephen's, as at other soup kitchens in the area, the tensions among people waiting to be fed "are much higher," says pastor Woodard.

Recently the church's security guard, a burly ex-Marine, took three knives from men waiting to get into the dining room, Woodard says, adding, "It's getting real hairy, let me tell you."