Four of the candidates supported by Mayor Marion Barry were elected to the D.C. school board yesterday, giving the mayor more influence over the board than he has had in the past, but still leaving him without enough allies to make up a majority on the 11-member board.

Barry has accused the current board, especially the members of its controlling faction, of sinking confidence in the public schools to an all-time low through its often rancorous behavior. In the aftermath of this spring's 23-day teacher strike, during which he had sharp disagreements with the board majority, Barry fielded his own slate of candidates.

At-large school board member Eugene Kinlow, 39, a personnel specialist for the federal government and former chairman of the Anacostia Community School Board, was the biggest winner among those on the Barry slate. Kinlow won over four other candidates by a lopsided margin.

Frank Smith Jr., 37, an urban planner and longtime activist in the Adams-Morgan area, ousted former board president Conrad P. Smith by a margin of nearly 2 to 1. Barry had supported Frank Smith. Three other candidates trailed far behind.

Linda W. Cropp, a 32-year-old high school counselor and the wife of Barry's executive secretary, Dwight Cropp, also turned an incumbent out of office. With the help of the Barry organization, Linda Cropp soundly defeated Victoria T. Street in the campaign to represent Ward 4, the upper Northwest.

Lawyer Nathaniel Bush, 30, won the only school board contest in which no incumbent was running. Bush, another candidate backed by Barry, defeated three other candidates in the race to succeed retiring board member Minnie S. tWoodson as the representative from Ward 7 in far Northeast and Southeast Washington.

Both of the incumbents who defeated candidates backed by the mayor were members of the old minority faction of the board, and both were endorsed by the Washington Teachers Union, which in all other cases supported the same candidates as Barry.

Bettie G. Benjamin, a lawyer and board member since 1974, defeated lawyer Matthew F. Shannon, a special assistant to the mayor, to win reelection as the board representative of Ward 5 in Northeast Washington.

In the closest race of the day, incumbent John E. Warren, 33, a public management analyst, narrowly defeated former PTA president Loraine Bennett in Ward 6, which includes Capitol Hill and the near Northeast, Warren won by 79 votes.

The outcome of that election was somewhat in doubt last night because there were 123 challenged ballots that will not be counted until next week. In the past, however, challenged ballots have generally mirrored the pattern of the regular vote.

City elections officials reported that 34,579 of the District's 241,711 registered voters took part in the election under clear skies and warm autumn temperatures. The voter turnout, about 14 percent, was larger than the 10 percent, was larger than the 10 percent common in city school board races, but fewer than the 50,000 persons who voted in 1977 when there were more registered voters in the city.

Five seats on the 11-member board were not on the ballot. Two at-large candidates will not have to stand for reelection until 1981, and there were no elections in wards 2, 3, and 8.

The new board alignment is an unpredictable patchwork of alliances. The four-member minority of the old board remains intact. The old six-member majority has been cut in half. Barry has four member ostensibly supporting him.

The Washington Teachers Union president, William H. Simons, and the outgoing board president, Woodson, said last night that there probably would be a new alignment of power. But it would not necessarily be under the control of Barry, they said.

Barry was unavailable for comment last night.

Meanwhile, election officials said there were no irregularities reported in the use of the Datavote punchcard voting system, which has only been used in all precincts in one other city-wide election.

In Ward 7, however, several school board candidates complained that some voters were pressured into voting for a particular candidate in the election. James L. Denson, chairman of the Board of Elections and Ethics, said those allegations would be investigated.

Yesterday's election was the seventh regularly scheduled vote for school board representatives since the city first began electing its own public education policy-makers in 1968.

Few real issues divided the 23 candidates. Even many of those endorsed Barry joined their opponents, for example, in criticizing a proposal by the mayor to reduce the school budget by $10 million next year because of declining enrollment.

Still, it was Barry's role in the race that increased the political ramifications of the voting, even though the posture taken by the mayor was less pronounced than that he assumed earlier this year when he successfully backed John Ray as his successor on the City Council.

The election took place during a time of continued concern about low student achievement in the public schools.

"Social promotions," in which students are advanced regardless of demonstrated skill once they reach a certain age, was frequently attacked. There were also calls for tighter oversight of the system's teachers. But the 23-day teacher strike of last March was not a major issue in the campaign. t

Barry asserted that school confidence was at an all-time low and that most of the current members of the school board, often viewed as embarrassingly bitter toward one another in public, was not a good role model for the city in its fifth year of home rule. His political strategists sensed a feeling in the city that incumbents could be defeated.

Some incumbents campaigned on counterclaims that they were doing a better job than many of their opponents claimed. Some openly criticized Barry's involvement in the ostensibly nonpartisan race for a supposedly independent board.

District voters also cast ballots yesterday for up to 366 representatives on the Advisory Neighborhood Commissions, the city-sanctioned program of grass roots community politics. Complete results of the ANC elections were not immediately available last night.