Delegates to the Democratic Party's midterm convention agreed today that Virginia's independent Sen. Harry F. Byrd Jr. should be deprived of his standing within the Senate Democratic Caucus.

And while supporters of the proposal within the Virginia delegation were cheered by their success, Democratic National Chairman John C. White said the action was only "an expression. It won't have an effect one way or the other" on the Senate.

The resolution, entitled "Democrats for Democrats," silpped through without discussion as restless delegates suspended the rules and jointly adopted 13 resolutions, including the one about Byrd, before going home this affternoon.

The resolution, proposed by Ira Lechner of Arlington, declares that "the Democratic Caucus of the United States Senate should be composed of Democrats only and not Republicans or independents." It does not mention Byrd by name, but he is the only independent in the Senate.

Lechner concedes that it is one thing to get party activists to pass that resolution and something else again to get Senate Democrats to go along with it. Although Democrats don't need Byrd's vote now to remain the majority party in the Senate, they might some day.

But Lechner said he considers adoption of the resolution "a mandate from the National Democratic Party." Because there was no previous policy statement on the matter, "it fills a vacuum," Lechner said.

Backers of the resolution, including nearly all of the 32-member Virginia delegation, say they also will try to have the statement incorporated in the 1980 party platform.

"If the Senate takes seriously what we just spent $1 million to do," (holding the party's second midterm convention), the Senate should seriously consider the resolution, Lechner said.

One effect of today's action, Lechner predicted, will be "to assure that the Democratic Senate Campaign Committee never again will contribute money to a Byrd campaign," as it did two years ago in his race against the party's own nominee, retired admiral Elmo Zumwalt.

Lechner said he already has discussed with several Senate aides here "which senator would be the most appropriate to carry the resolution" to the caucus when it meets next month as the 96th Congress begins.

"If we approach a senior senator, he would have more clout, but he also may feel strongly that Byrd is a member of the club," Lechner said. "A freshman senator might be more responsive."

Virginia Democrats are primarily concerned about the power Byrd now has to recommend appointments to federal judgeships and other positions of influence. But his tenure and his membership in the caucus also combine to deprive Democrats who have not been in the Senate as long as Byrd seniority on Senate as long as Byrd seniority on Senate committees.

The resolution was endorsed at a Virginia delegation caucus here Thursday night. Although there was little discussion and no recorded vote, Lt. Gov. Charles S. Robb, H. Benson Dendy III of Robb's staff and L. Ray Ashworth of Wakefield were known to be among the few opponents.

The Democrats-for-Democrats resolution was the only one not on the original agenda that was adopted by the convention. Backers of the measure had to secure signatures of support from 409 delegates to obtain consideration of the proposal. They got 634.

A second resolution, which did not go beyond the state delegation, invites Byrd to return to the Democratic Party, but that is an invitation that he has ignored repeatedly.