Senate Majority Leader Robert C. Byrd suggested yesterday that Energy Secretary James R. Schlesinger get his act together on the gasoline-shortage story before his credibility is gone.

Like most everyone else these days, Byrd told reporters, he is not quite certain what to believe of the information coming out of the Department of Energy.

"I've been frustrated and confused by conflicting statements and statistics coming out of the DOE and, more recently, the White House as well," Byrd said.

Byrd declined to go as far as some other congressional critics who have called for Schlesinger's dismissal, but he said overall confusion is creating serious problems of trust and credibility.

"We hear conflicting stories out of DOE and the White House . . . optimistic reports one day, pessimistic reports the next day," he said.

"Too much confusion leads to distrust of government, to distrust of government's ability to deal with the situation. There's going to have to be an improvement in the Department of Energy, lest that distrust grows."

Byrd said there "needs to be some getting of the act together in the department," although he conceded that Schlesinger's job is a "tough" one that he wouldn't care to take on.

If the West Virginia Democrate is "frustrated and confused" about DOE, the message he got from Mrs. Byrd last week about gasoline was loud and clear: She had to go to 12 stations in Northern Virginia before she could gas up the family car.

Repeating a plea he made a week ago, Byrd urged President Carter to call together congressional energy leaders-Democrats and Republicans-to work out an agreement on a standby gasoline rationing plan.

Even though the House killed Carter's proposed plan two weeks ago, Byrd said he thinks an agreement could be hammered out if the president took the lead in "getting the pieces together."

"Nobody wants to vote for a rationing plan," he continued, "and Congress has a responsibility in this-but it is not alone. The executive branch also has a responsibility . . . to protect the public in case of an energy emergency."

The White House reacted coolly last week to Byrd's call for a "summit"-type of meeting to work out a gasoline plan. Carter, critical of the House vote that killed the administration plan, had challenged Congress to come up with a plan of its own.