The Republican with the best chance to loosen the Democratic party's stranglehold on local Washington politics may be Ward 5 city council candidate Ron Evans.

Still, the best of the Republicans may not be enough to beat any Democrat. While Republicans are the second strongest party in the city in terms of money and organization, they hold only three of the city's 25 major elected offices, those of At-Large City Council member Jerry Moore and two school board members, Bettie Benjamin of Ward 5 and Wanda Washburn of Ward 3.

If any of the five Republican candidates for office have a chance of victory Tuesday, however, it is W. Ron Evans. Insiders give the 44-year-old real estate broker who has lived in the city 25 years the best shot of any Republican at winning.

"We're counting on a whole lot of discontent with the Democrats," said Robert S. Carter, chairman of the D.C. Republican Party. "There's more discontent with Ward 5 Democratic council member William Spaulding than with any of the other Democrats. He's got to take a lot of the blame for the problems with the elections as head of the council's Committee on Government Operations, which oversees the elections board , and Ron Evans is an appealing candidate."

The Republicans' other high-profile council candidate is Lois DeVecchio, candidate for the Ward 3 seat on the council. The ward, which includes the affluent neighborhoods west of Rock Creek Park, holds the city's highest concentration of Republicans and is the only ward with its own local GOP organization. But DeVecchio's opponent is Democrat Polly Shackleton, a political fixture.

That leaves Evans, whose bid to represent the mostly middle-class neighborhoods of Northeast Washington is his first try for political office, as the city Republicans' great hope this year.

But Evans is not exactly waving the Republican flag for all to see. He doesn't use his party affiliation on his literature and signs, and when asked what help he is receiving from the D.C. Republican party, he shakes his head.

"If I were depending on the Republican Party, I'd really be in trouble," Evans said at the 12th Street NE office of a recreation group, Black Ski, that doubles as his campaign headquarters. "Of the 50 to 60 campaign workers we have, two-thirds of them are Democrats."

Evans also distances himself from the Republican in the White House. One recent morning he told commuters at the Brookland and Fort Totten Metrorail stations that the only thing he and Ronald Reagan have in common are their first names and the party.

To try to prompt blacks, whom polls have shown are particularly angry at Reagan's policies, to vote for him despite his being a Republican, Evans has his telephone bank workers tell voters blacks have to get involved in two-party politics or the Democrats will be up to no good at the District Building, confident of support whether or not they deserve it.

That speech leads to Evans' campaign theme, which sounds very Republican. He promises to work to give businesses tax abatement and other incentives to stay in the ward and expand. He says New York Avenue NE has gone undeveloped under the Democrats, although studies have shown it is a prime area for light industry.

Evans points out to voters that the ward has lost four Safeway supermarkets, a Giant store, an A&P and a Sears. The departure of Parsons Paper Co., International Distributors and other companies cost the ward additional jobs, he says.

But try as he may to put out his proposals without attaching any party label, Evans can't escape Spaulding's nonstop reminders to voters that they are dealing with a Republican.

"The Republcian party stands for unemployment," Spaulding has repeatedly told voters. "It stands for reduced grants to D.C. The Republican Party stands for increased interest rates . . . and he is a Republican."

For Evans to win, he would have to attract a large number of crossover votes from the Democratic party.

Republicans believe that feat is possible in Ward 5 because of Spaulding's history of barely surviving his Democratic primary contests against crowded fields of challengers. In the September primary, Spaulding won over four other contenders by fewer than 1,000 votes, garnering overall only about one-third of the votes cast.

Still, that margin of victory is the largest Sapulding has enjoyed in his primary battles. In 1978 he won by only about 300 votes. But in the general elections he usually has won handily, facing no substantial opposition prior to Evans in this general election.

Evans is building his campaign strategy on expectations that at least half of the 11,000 Democrats who did not vote for Spaulding in the primary will vote against him in the general election, although Spaulding has easily survived serious Republican opposition in the past. Evans also hopes to capture the Republicans and independents who total about 12 percent of the ward's voters.