The Bradys, Brennans, Caseys, Daileys, Delahantys, Kennedys, Murphys, O'Learys, Regans, Ryans, Shannons, Stantons and dozens of other sons and daughters of the old sod had lunch with two of their own kind at the White House yesterday. They were part of President Reagan's own St. Patrick's Day parade, invited in to meet Irish Prime Minister Charles Haughey.

Elected only a week ago, the 56-year-old leader of the Fianna Fail party, with his wife, Maureen, arrived Tuesday from Dublin with a special appeal for his host to urge Britain to begin "her final withdrawal" from Ireland.

Wearing a green necktie and a spray of shamrocks in his lapel, President Reagan did not touch upon Northern Ireland's political problems in his after-luncheon toast (although he did issue a statement during the day calling for reconciliation). Reagan touched on his own political problems, though, when he said Rep. Robert Michel (R-Ill.) had given him a shillelagh "and suggested I might use it to get legislation through the Congress."

The congressional delegation did not include the president's Irish nemesis on Capitol Hill, House Speaker Thomas P. (Tip) O'Neill, who sent his regrets because of "a prior commitment."

The pink cheeks of President Reagan, great-great-grandson of Michael O'Regan, who came from County Tipperary, glowed even brighter when Haughey presented him further documentation of his Irish beginnings.

"The Reagans were 'the defenders of the hills' and for more than seven centuries against all comers they held the only pass through their territory of Y Regan in the Slieve Bloom Mountains," Haughey told the president. "They held it against friend and foe and the English, at one stage of their long and unsuccessful efforts to conquer our country, paid the O'Regans a great compliment. Their commanders, methodical men, prepared and sent London maps on which were marked the names of the most redoubtable Irish chieftains--those from whom the strongest resistance was to be expected."

Holding up a framed photographic print of such a map dating from 1565 and showing the Reagan origins, Haughey said: "I present it to you, Ronald Reagan, 'defender of the hills,' president of the United States of America and friend of Ireland."

The president appeared moved by the presentation and then added, "Prime Minister, I realize I'll be threatened with investigation of my income tax unless I share it with Treasury Secretary Don Regan."

At the president's table, where Irish potatoes sprouted shamrocks as part of the floral centerpiece, were the Haugheys, First Lady Nancy Reagan, actress Maureen O'Hara, Sen. Paul Laxalt (R-Nev.), newly confirmed Ambassador to Ireland Peter Dailey Sr., and opera singer Eileen Farrell. At the next table with Vice President Bush was Sen. Edward M. Kennedy (D-Mass.), who told reporters when he arrived that he did not think "the Kennedys of Wexford met the Reagans of Tipperary."

At another table with Rep. Clement J. Zablocki (D-Wis.), chairman of the House Foreign Affairs Committee, was presidential assistant and press secretary James S. Brady and his wife, Sarah. Elsewhere was Sen. Charles Percy (R-Ill.), head of the Senate Foreign Relations Committee.

"I don't know what I'm doing on the list," deadpanned Percy, who said the only Irish connection his English ancestors had was "we fought 'em."