When the seven women visitors from California called at the office of Sen. Alan Cranston (D-Cal.) one day last month, they went through the usual tourist ritual of having their picture taken with the smiling senator.

Then the women engaged the legislator in a brisk discussion of the SALT II treaty and of the Water Reclamation bill.

The visitors were not ordinary tourist, but Roman Catholic nuns who were in town for a legislative seminar - an intensive week-long training course on how to use the political process to achieve their visions of a better world.

From Cranston's office, where they found a warm reception for their pro-SALT views, the nuns made a fruitless effort to pay a similar on Sen. S. I. Hayakawa (R-Cal.) whose staff had declined a request for a meeting. Then they fanned out to keep other appointments.

Sister Jeanmarie Montgomery, the assistant principal and dean of discipline of a Catholic high school in Burlington, Cal., walked over to the Capitol's east steps, picked up a picket sign that said "NIX THE MX" and joined a demonstration by fellow participants in the seminar supporting the SALT II treaty but opposing the MX missile. Both the demonstration and the lobbying appointments with legislators were part of the seminar program.

More than 200 persons, most of them nuns, from 37 states took part in the week-long seminar, which was sponsored by Network, a 7-year-old organization founded and operated by Roman Catholic sisters. Network has a reputation for being one of the most effective members of the religious lobby.

One of the more unusual special interest groups on Capitol Hill, the religious lobby operates in many cases on shoestring budgets and readily acknowledges that, in general, it probably has only a marginal influence on legislation.

About 100 men and women are involved in the religious lobby. Although some of their efforts are directed at such obvious institutional interests as aid to parochial schools, many others focus on "social justice issues."

Participants in Network's legislative seminar spent 12 hours a day listening to discussions, many of them led by members of Congress, on issues such as disarmament, housing, foreign aid, energy, health care and food policy.

Before they were unleashed to lobby on Capitol Hill on the next-to-last day of the seminar, the participants were carefully briefed on such topics as "How a Bill Becomes a Law," "How to Lobby" and "Strategize for Lobbying."

In addition, participants were given packets of background papers about a dozen bills before Congress, another packet detailing how members of Congress voted on selected issues within the past few months, and a sheet entitled "Tips on Lobbying," with detailed suggestions and lists of "Do's" and "Don'ts."

When she goes back to California next month, Montgomery will try to follow what she said was Cranston's advice to the nuns who came to visit him: work to mobilize Californians to pressure their other senator - Hayakawa - to support SALT II.

Network's membership list - 4,300 - is miniscule compared with major public interest or lobbying groups. However, there may well be a significant muliplier effect, since most of the members live or work in communities of Catholic nuns who share both the legislative materials and Network's enthusiasm.

In addition, the computerized membership list is indexed both by state and by Congressional districts, so that pressure can be mounted on selected areas as the political situation dictates.

The Roman Catholic Church, with 50 million members scattered through every state, is theoretically one of the most formidable pressure groups in the nation.

But any parish priest will say that there are few, if any, issues that a local congregation, let alone the entire Catholic population, will unite behind. Even such traditionally Catholic issues as aid to parochial schools or anti-abortion legislation fail to elicit from Catholics full agreement and support when transformed into legislation.

So, the National Conference of Catholic Bishops maintains a government liaison office, both to ensure that the interests of Catholic institutions are protected when laws are written and interpreted, and to impress on legislators official Catholic views of a good and just society.

"The Catholic Church has a very high level of moral criteria for human activity," said the Most Rev. Thomas C. Kelly, general secretary for the Bishops' Conference. "Anyone who wants to do good legislation ought to know what they are."

Members of Congress and their aides who help to draft legislation have, over the years, become aware of the church's interest in a wide range of legislation and often seek out those views on particular issues.

Representatives of the bishops appear before committee of Congress 30 or 40 times a year to present testimony.

Most often, one of the staff experts in domestic or foreign affairs takes on the assignment. "If it's an important issue, we may bring in a bishop to raise the visibility and make it a bit more dramatic," said Msgr. Francis J. Lally, who directs the conference's department of social development and world peace.

Several years ago, in the wake of the Supreme Court decision legalizing abortion, the conference deemed the issue so important it brought in three cardinals to testify in favor of outlawing abortion.

The presence of the high church leaders in the hearing rooms did indeed dramatize the issue and bring out the TV cameras. But the right-to-life movement has been struggling ever since to erase the impression by the massive Catholic presence that the battle against abortion is a Catholic battle.

Members of Congress give the religious lobby mixed reviews. Sen. Frank Church (D-Idaho), chairman of the Foreign Relations Committee, said the lobby "tends to be effective on many issues."

He said religious lobbyists make their greatest contribution in social welfare reform, food relief abroad, and areas where they speak for the moral concerns of the world at large.

Sen. Mark Hatfield (R-Ore.), however, said "I have never been overly impressed with any religious lobby. .... They are not necessarily speaking for the constitutency which bears the same name."

Rep. Robert Drinan (D-Mass.), who is a Jesuit priest calls Network "terrific." The members are among the most effective of the religious lobbyists, he said, "because they know what they're doing" both in terms of their lobbying tactics and their grasp of the issues.

The church hierarchy's man who spends the most time on Capitol hill is James L. Robinson, the director of the Conference's government liaison office. But Robinson rarely ventures far enough into the limelight to testify before a Congressional committee.

A former newspaperman whose name rarely appears in the church's press releases, Robinson sees his role as a sort of ecclesiastical watchdog, ready to sound the alarm over any proposed legislation or regulation that threatens to involve the church or its institutions.

Robinson sidestepped a question of whether institutional concerns or social justice issues receive more attention by his staff. "You can't separate the two," he said.

To illustrate his point, he cited an issue that came up earlier this year when the U.S. Department of Labor, under threat of a lawsuit charging violations of Constitutional guarantees of church-state separation, cut off Comprehensive Employment and Training Act (CETA) programs from Catholic schools. The church fought back.

"The purpose of our institutions being involved in CETA was to help people who are the rejects of society, people who have been turned down by the institutions of society," Robinson said.

Last April, when the cut-off occurred, Bishop Kelly publicly protested and Robinson's office began quiet negotiations with the Labor Department. Late last month, the Department proposed rules that would bar CETA workers from some tasks in parochial schools, but would allow them to work in such areas as food services, or as health or safety aides or in the administration of federal or state programs.

On the question of the militant anti-abortion political groups which have organized around the single issue of electing candidates pledged to support anti-abortion legislation, Bishop Kelly, who is Robinson's immediate superior, is careful to distinguish such groups from the hierarchy.

"Catholic teaching on abortion is very clear," he said, "but there are many, many ways to approach the question politically."

He said the right-to-life movement, which has targeted for defeat many of the members of Congress who have given strongest support to social justice issues, "is a citizen's movement." The hierarchy's educational material, he said "deals with all the issues of respect for life," not just abortion.

Network's nuns are more aggressive in combatting the right-to-life movement's "hit list" and evaluating instead a legislator's over-all record on social issues.

An entire session at Network's legislative workshop was devoted to "Multi-Issue Approach to Election '80." Complete with slides and charts, it featured a voting analysis of social justice issues other than abortion. The legislators on the hit list - men like Sens. Birch Bayh (D-Ind.), Church, John C. Culver (D-Iowa) and Reps. Drinan, Robert Edgar (d-Pa.), and Morris Udall (d-Ariz.) - received very high ratings from network while right-to-life favorites such as Senators Orrin Hatch (R-Utah), Jesse Helms (R-N.C.), and Jake Garn (R-Utah) barely made it onto the chart.

Sister Carol Coston, founder of Network andits executive director, made it clear that while her organization fully agrees with Catholic teaching on abortion, the politicizing of the issue is worrisom.

"I don't care if they ask (candidates") positions on abortion, but let's ask for their position on, say, 20 other issues" on which the church also has established positions, she said.