Virginia Democrats are asking the Democratic National Party conference here for help in stripping Harry F. Byrd of the privileges he gets by voting with the Senate Democratic caucus.

Byrd, the Senate's only independent, is chairman of two subcommittees and has patronage power that he would not get if he were treated as an independent instead of as a member of the majority party.

The Virginia resolution was introduced by Ira M. Lechner, a labor lawyer from Arlington, and was supported in a voice vote by all but about three of the state's 32-member delegation.

One of the opponents is Lt. Gov. Charles S. Robb, the only Democrat holding a statewide office in Virginia. Robb was not present when the resolution was discussed by the Virginia delegates.

Robb said tonight he favors the approach supported by State Del. L. Ray Ashworth of Wakefield, who got the delegation to adopt unanimously a second resolution today that invites Byrd to return to the Democratic Party.

"We've invited him back many times and he never even bothers to answer us," said Sumiko Biderman of McLean. The anti-Byrd resolution sponsors must get one-fourth of the 1,600 delegates who are attending this midterm convention to sign petitions before the resolution can be placed on the agenda of Sunday's voting session.

Robb said that while he understands "the sense of frustration" felt by the delegates who are among the party's most active members, he believes adoption of the anti-Byrd resolution would be "misconstrued as a signal" that the party wants to exclude people who agree totally with the senator.

But Biderman said, "Those of us who work in the vineyards work to elect Democrats." She said the fact that President Carter "goes to him" (Byrd) for nominations for federal judgeships in Virginia demonstrates the power Byrd gets by being extended privileges reserved for the senator of the president's party.

Biderman said that many Virginia Democrats were angered by a poster distributed in the recent Senate campaign that showed Byrd with Republican John W. Warner, who won the close election over Democrat Andrew P. Miller Jr.

Christie Vernon, a delegate from Grafton near Newport News said it is "outrageous" that Byrd gets "money, rank and all that accrues" to the majority party and gives no quid pro quo. She said that Byrd even got $5,000 from a Senate Democratic fund when he ran against Democrat Elmo Zumwalt two years ago.

Some Democrats worry that if Byrd is pushed, he might follow the lead of former Democratic Gov. Mills E. Godwin and join the Republican Party, Vernon said.

But even the anti-Byrd resolution's most avid supporters believe its passage here is likely to have little impact on Senate Democrats. "Even Teddy Kennedy won't vote for it," Vernon said.

Backers of the resolution nonetheless fanned out through the various state and issue caucuses here today, soliciting signatures on petitions. And while most of the delegates from other states who were unaware of the situation reacted enthusiastically, some refused to sign, Vernon said.

Maryland Acting Gov. Blair Lee III declined, telling Biderman that Byrd was an old friend.

Martha L. Goyette of Williamsburg said most of the delegates here "find it totally reasonable that the Democratic caucus should be limited to Democrats."

Byrd's press aide said tonight in Washington that the senator was aware of the resolution but said "no comment" on it.

Meanwhile, delegates from the District of Columbia were drumming up support for their special concern, the D.C. voting rights amendment.

The proposed constitutional amendment that would give the District two senators and one or two House members is the subject of one of the resolutions already on Sunday's agenda. Delegates from the District are hoping to get pledges from delegates to work for ratification of the amendment in their home states.