It was goodbye Joe and goodbye Brock at two farewell parties last night where absolutely nobody cried. That's because everyone was too busy drinking champagne, cooking up pithy one-liners and even singing for Joseph Califano, fired Health, Education and Welfare secretary, and Brock Adams, fired Transportation secretary.

In fact, nobody even minded that Adams was 40 minutes late to his own party, a breach of etiquette he blamed on a transportation problem he couldn't solve -- one stuck elevator. "I work horizontal transportation," he apologized.

Both parties were on Capitol Hill. Califano hd his in a small House reception room where he greeted a steady stream of representatives plus two "imposters," as he called them -- Sens. Edward Kennedy (D-Mass.) and Richard Schweiker (r-Pa.).

And then the singing started. Led by House Speaker Thomas P. (Tip) O'Neill Jr., a quartet of representatives including Leon E. Panetta (D- (Califf.), Marty Russo (D-Ill.) and Thomas Joseph Downey (D.,N.Y. sang an ode of sorts. It was called "Amore Southern Style," a bastardized version of "That's Amore" which Dean Martin used to sing. Panetta wrote this one.

"When old Jimmy hits you eye with a big fat goodbye. . .That's amore;

"When ole Ham says you fine but he kicks you in the behind . . . That's amore;

"Phones will ring. . . ding-a-ling-a-ling .. .ding-a-ling-a-ling. . .and they'll sing 'nice-a fella';

"Staff will play . . . tippi-tippi-tay . . . tippi-tippi-tay . . . and they'll say go to hel-la.'

"When you think you're number one . . .but the president says 'ya'll done . . .signore;

"Scusa me but you see . . . back in the ole Confederacy . . .that's amore . . . amore . . . amore."

And with that, this Cabinet member of Italian descent was presented with a casserole of lasagna, made by Downey's wife, Chris, and inscribed with noodles that said "Good Luck Joe."

"Why should we be sad?" said Rep. Peter W. Rodno Jr. (D-N.J.) "Here's a man who's had a distinguished career."

"It isn't like a wake," said Rep. Norman D. Dicks (D-Wash.). "I think people really truly have a great affection for Califano."

As for Califano, he laughed, drank champagne, slapped backs of congressmen and kissed the cheeks of female Hill staffers.

His plans, come noon Friday when he's gone from the office for good? "Lunch."

And after lunch? Well, if Califano didnt have any ideas, one congressman did.

"He's going to run for the U.S. Senate seat from New York," said Rep. John J. LaFalce (D-N.Y.), who volunteered to be campaign director. "The first thing we're going to do," LaFalce continued as he patted Califano's stomach, "is make him lose about 10 or 15 pounds. Then he's going to have to go back to the Brooklyn accent." Califano laughed.

Across the street at the Longworth House Office Building, people were gathering for the party hosted by the Washington state congressonal delegation.

Everybody stood around and ate, waiting for Brock Adams. Some of them grumbled about Jimmy Carter.

Rep. Richard Nolan (D-Minn.), who has called on both Vice President Mondale and Sen. Kennedy to run for president, was critical of Carter. "I think he's just pathetic," said Nolan. "O presidency is just all washed up I think he's a lame duck.

And then, finally, Adams arrived. The television crews swooped, lights glaring, and Adams, acting like a hero who'd come home, related that he'd spent the past 20 minutes in an elevator on the basement floor.

"Isn't that terrible?" he laughed to Rep. Al Ullman (D-Ore) "What a day."

Also stuck were four interns from Sen. Henry M. (Scoop) Jackson's (D-Wash) office who didn't even know that the other man in their elevator was really Brock Adams.

"We didn't recongnize him, you know, because we were all a sort of smooshed in," said one staffer.

"Oh, he was so cute," said another.

Once he got to his party, Adams acted a lot like Califano: he hugged, drank champagne, and made an announcement that he could always use new clients in a law practice he plans to open.

There seemed to be little resentment on his part, even though he and Carter parted on less than friendly terms.

"I have neither feelings of bitterness, nor feelings that anything's wrong," he said. "It's really more a feeling of relief -- like being in a decompression chamber. CAPTION: Picture, Brock Adams, left with Rep. Al. Ullman by Joe Heiberger