National Airline shareholders voted overwhelmingly today to merge with Pan American World Airways pending final government approval.

But the shareholders also voted to permit a bidding war between Pan Am and Eastern Airlines if both carriers obtain government approval to acquire National.

Nearly 80 percent of National's outstanding shares were voted in favor of the management-supported proposals.

Pan Am's and Texas International Airlines' nearly 50 percent stake in National was voted proportionately under a trust agreement approved by the Civil Aeronautics Board.

As National Chairman L. B. Maytag noted before the meting today, however, the vote is "meaningless" unless the merger is approved by both the CAB and President Carter. The CAB, which has scheduled an oral argument on the merger proposals for June 22, has said it will try to make a decision shortly after that.

If Pan Am does get regulatory approval, today's shareholder vote means that each stockholder of National would receive $50 cash for each share of National common stock. If Pan Am does not receive approval for the merger but Eastern Airlines does, the proposal adopted today authorizes National to enter inot a merger agreement with Eastern at $50 a share.

If both Pan Am and Eastern get the government go ahead, and Eastern raises its cash offer above the $50 a share mark, Pan Am must match Eastern's raised offer or National is free to merge with Eastern at the higher price.

Should Pan Am agree to match a higher Eastern offer, then Eastern and Pan Am may participate in an auction bidding process with the winner acquiring National, although Pan Am gets the last bid.

The only major party left out of the merger plans adopted by shareholders today is Texas International Airlines, the small aggressive airline that started the scramble for National when it picked up 9.2 percent of National's stock last July.

If Texas International alone gets government approval for its acquisition bid, it would have to proceed with a hostile tender offer over the objections of National's officers, who have been against its bid from the beginning.

At today's meeting, Maytag reiterated that the board of directors "is opposed to any merger with Texas International" and warned that if the Texas carrier gets government approval, "we cannot provide assurances as to what might happen-whether you be stockholders, employes, communities we serve or the traveling public."

A fourth contender, Air Florida, has offered to acquire National's international route authority an four DC-10 aircraft for $110 million should the CAB want to allow Pan Am to pick up National's domestic route system, but balk at combining the two airlines transatlantic routes.

In a company statement issued after the National meeting, Texas International said that in spite of the shareholders action it would continue to "vigorously prosecute its own case for approval to acquire control of National before the CAB, which has the ultimate power to decide this case."

William T. Seasell, Pan Am's chairman, said he was "optimistic . . . I believe we have shown that a Pan Am National merger meets the aims of deregulation and will provide significant public benefits."

Eastern's chairman, Frank Borman, said he was pleased with the vote and was confident that the CAB would "respond to it in the free enterprise spirit mandated by the Airline Deregulation Act." CAPTION: Picture, National Airlines Chairman L. B. Maytag conducts yesterday's meeting. AP