President Carter, whose relations with organized labor have been something less than festive, has invited the nation's top union leaders to what has been billed an "old-fashioned Labor Day picnic" on the South Lawn of the White House next Monday evening.

It is the first time since former president Nixon set out to court the blue-collar vote during his first term that such a Labor Day celebration has been planned for the White House.

The invitations offer hamburgers, hot dogs and "games", which has caused some amusement in union circles in light of the average age of most union leaders."You could alter half the membership of the AFL-CIO Executive Council with one energetic volleyball game," said one unionist yesterday.

Volleyball is indeed planned, along with softball and other "old-fashioned games," according to a Labor Department official.

A White House press aide said that about 1,000 people are expected to attend the 6-to-9 p.m. picnic, primarily from the "labor movement community" but also including members of Congress, department of Labor officials and others.

The invitations came in the midst of an intensive effort by the White House to mend fences with labor leaders, many of whom, including AFL-CIO President George Meany, have disagreed sharply with Carter on economic and other issues. A half dozen or so union presidents have signed up with the Carter reelection effort, and administration officals have been courting others.

AFL-CIO spokesman Albert J. Zack said Meany, who just celebrated his 85th birthday and is recuperating from a hip ailment, plans to attend if he feels up to it. The federation's second-in-command, Secretary-Treasurer plane Kirkland, is planning to go, Zack said. "We expect a whole lot of people will be going," Zack added.

One who won't is William H. Winpisinger, president of the International Association of Machinists and Carter's most acerbic labor union critic. A Winpisinger aide said the union "as an institution" was sent an invitation but that no one from the IAM will be going. Officials of the International Brotherhood of Teamsters, who were excluded from at least one other White House labor gathering, have been invited, an administration source said.

The White House said both President Carter and Mrs. Carter, who will be returning from their home in Plains, Ga., on Monday, will attend.