Voters in the District, Virginia and Maryland are expected to turn out today in near-record numbers, despite a generally acknowledged lack of suspense over the presidential contest.

Republican campaign workers believe they have a chance to capture traditionally Democratic Maryland for President Reagan.

In Virginia, voter interest has been stirred by House contests in which Democrats hope to pick up seats, as well as by the race between first-term Republican Sen. John Warner and challenger Edythe C. Harrison, who trails badly in the polls.

The District has a hotly contested City Council race, along with a controversial ballot measure on sheltering the homeless.

Harrison, who has been outspent by Warner 6 to 1, yesterday canceled several scheduled appearances in Northern Virginia because of threatening weather and instead went to Virginia Beach, where she planned to attend an evening rally with Democratic Gov. Charles S. Robb.

In the District, election officials have predicted a record turnout of 200,000 voters, with the main event the contest for one of two at-large seats on the City Council.

City Council member Jerry A. Moore Jr. (R-At Large), who was defeated by former school board member Carol Schwartz in the Republican primary, is waging an unusual write-in campaign that has the support of the city's Baptist ministers and much of Mayor Marion Barry's potent Democratic orgnization, but not of labor groups that are backing Statehood Party candidate Josephine Butler.

In the final weeks of the campaign, Moore and Schwartz each have spent about $9,000 in radio commercials.

Jesse L. Jackson, who won the District's May 1 presidential primary contest, speaks in one of Moore's commercials, encouraging residents to "write in and punch" Moore's name.

Schwartz said that Marcelo Fernandez, chairman of a Hispanic group that supported Barry's reelection in 1982, recorded one of her radio spots in Spanish.

Meanwhile, the District government made a last-minute push against a ballot initiative that would guarantee adequate overnight shelter to the homeless.

The D.C. Office of Intergovernmental Relations mailed out a two-page "fact sheet" to about 1,500 members of District boards and commissions, stating that the initiative "would have a detrimental effect on the city's ability to provide comprehensive services to the homeless and other needy individuals" and that it would "result most likely in a tax increase for District residents."

Steve O'Neil, a member of the Community for Creative Non-Violence, charged that the mailing is an inappropriate and illegal use of government funds to oppose an initiative.

Pauline Schneider, director of intergovernmental relations, said that the city was careful in its mailing not to state a position for or against the initiative. And Keith Vance, director of the Office of Campaign Finance, which oversees election laws, said that "it does not appear there is any violation of the campaign statute" in the city's distribution of the fact sheet.

Jeff Stake, a Covington & Burling attorney representing the Committee on Overnight Shelter that supports the initiative, said yesterday it was too late to do anything about the city's mailing, which he said "is not the city's proper role."

There is another write-in campaign of note: In Virginia, the "New Right" wing of the divided Fairfax County Republican Party is waging a heavy last-minute write-in campaign for a little-noticed seat on the board of directors of the county Soil and Water Conservation District.

The board traditionally has been considered a nonpartisan body.

Sample ballots urge voters to cast write-in votes for Gloria Fisher, the candidate who unsuccesfully sought the Republican nomination for the hotly-contested Mount Vernon seat on the county Board of Supervisors.

Some of the county's moderate Republicans say they believe Fisher would use the position as springboard for a future political career -- speculation that Fisher discourages.

In Baltimore, volunteers for the Mondale-Ferraro campaign distributed all their leftover literature in the Inner Harbor and Lexington Market yesterday.

Volunteer crews also were out in West Baltimore, erecting campaign signs. And a number of telephone banks manned by representatives of organized labor, nuclear freeze advocates and women's groups continued dialing for votes.

The Maryland Republican Party, meanwhile, buoyed by the possibility of victory for Reagan in a traditionally Democratic state, pulled out all the stops.

Volunteers, many of them college students, distributed about 100,000 pieces of literature around the state urging voters to support the Reagan-Bush ticket.

The state's Republican Party had 350 telephones in operation.

In the 2nd Congressional District, where the GOP has its best chance of gaining a seat in Congress, Republican candidate Helen Delich Bentley spent the day knocking on doors and campaigning at a senior citizens center.

Bentley, who is running against 11-term Rep. Clarence D. Long, also launched a last-minute radio ad that features Vice President Bush, who campaigned for her in Baltimore County on Saturday.

Bentley's aides said that the commercial would run nine times in the 24 hours before the election.

Long, meanwhile, campaigned at office buildings in the district.