Moving lightly on his feet, very lightly, almost as if he were on eggs, I. Irving Davidson flits around his desk to touch the upper arm of a visitor. The touch is light as the walk, inviting confidentiality, promising discretion. The look is sharp, but not too sharp; dark suit, rounded gold jewelry, crisp white shirt. The face . . . you've seen it in the various corridors of power, elfin even at 59, always slightly in the shadow but always smiling, as if Irv Davidson knows something that the rest of us can only guess at: the ultimate Inside Story.

"Listen. If I get knocked out of the box it's going to hurt this country." A wink. A squeeze. The hint of anonymous contact, vague yet crucial understandings. "I'm involved in some very sensitive stuff overseas. I'm talking to people who our own people can't talk to."

For the second time in his long career as the Handy Andy of behind-the-scenes Washington, promoter-lobbyist Irv Davidson may be in trouble with the law. Trouble means publicity. Publicity is anathema to the back-channel function: "You can't operate with it. I'm looking for deals. I put people together. I work on a very personal level."

Indeed. Two people the FBI recently said that Davidson has "put together" are reputed New Orleans Mafia boss Carlos Marcello and Mario T. Noto, the former No. 2 man in the Immigration Service. Result: The FBI is investigating allegations that Noto acted improperly to help Marcello fight deportation. Davidson also introduced his "old friend" Marcello to another of his old friends who later turned out to be an undercover informer posing as an insurance salesman in the FBI sting scam Operation Brilab, which surfaced in February. Result: The FBI is investigating allegations that public officials ranging from Louisiana Lt. Gov. Jimmy Fitzmorris to Texas House Speaker William Clayton accepted illegal money. Fitzmorris and Clayton have testified before grand juries in connection with Brilab.

So Irv Davidson is walking like a cat on eggs. FBI agents grilled him for four hours Feb. 8 and told him they had bugged his phone for a year before that. He is under investigation. Suppose he is subpoenaed himself? Suppose there is a leak? Suppose . . . "I deal in confidentialities. If it gets out that I talked a lot, if my friends start thinking I have a big mouth . . ." Mr. Witty

Ah yes. The friends of Irv Davidson. Columnist Jack Anderson is as well acquainted with them as anybody.

"Your first impression of Irv is that he's a cheap operator," Anderson has said. "But when you get to know him you find he's got better contacts than Clark Clifford or any other St. Louis smoothie. In fact he's got unbelievable contacts. I'd call him unique. I've investigated a lot of five percenters and promoters but I've never ran across anybody like him."

Davidson's array of business cards say everything from "public relations" to "door opener and arranger." Of course there's no official name for what he really does . . . which is wheeling and dealing without a net, pedaling his lonely little bicycle across the tightrope hundreds of feet above the center of the ring. Usually in darkness too: No illumination for Irv. He's the grease in the machinery, the Grand Central switchboard operator. His stock in trade is being "witty," as they say in the CIA to describe someone who is aware of the various covert maneuverings. He claims that knowing the right Inside Story for everybody is now worth $250,000 a year.

Now certainly people like Clark Clifford must know a good piece of the Inside Story themselves, but they are too big, solid and respectable to make it into all the corners. Clifford would look out of place in the redbroaded twilit Gaslight Club with it's neo-bunny waitresses that the behind-the-scene set love so much. Whereas Davidson is not only on a first name basis with practically everyone there, but also with the hard core at Sans Souci, the Sheraton-Carlton Hotel Bar and the Georgetown Inn.

Jack Anderson, and before him Drew Pearson, not only calls Davidson but rented office space from him in the past. He was the first person Anderson called when Teamster boss Jimmy Hoffa dissappeared and when Marcello was reported to be back in the country after deportation to Guatemala. When Anderson wanted to talk to Bobby Baker, Davidson actually brought Baker into Anderson's office. In the end Davidson's maneuvering to capitalize on his Anderson connection forced the columnist to issue careful instructions: "Nobody is to say anything that Irv can use for promoting himself." 'Fidel Knows . . ."

Even now, with the heavy faatsteps of the FBI echoing in the corridor, Davidson will talk about deals with an almost frighteningly irrepressible banty pleasure:

"Who needs to get mixed up in this horse . . . . with Immigration?" He waves his hand around his office, which is full of totems from various deals -- model tanks and planes, plaques of quotations, trick paperweights, carved wooden statues. It looks like the bar at the 21 Club in New York. "Look what I have going. I'm bringing the Coke soft drink team into Sudan to show them how to grow citrus in the desert. I sold Clint Murchison's oil pier to the Malaysians when nobody else could even talk to them. I just borrowed $1 million for six months on nothing but pure bull."

The little tank is his favorite story: "An Israeli Staghound tank, see. I sold 70 of these to Nicaragua from Israel and then we decided to sell 20 of them to Batista in Cuba.We got them in shape, we put them on a Swedish boat to Havana and guess what? Castro got hold of them. Next thing I know he's riding into the city of Havana on one of our tanks. Now, there's an ending to this story going to knock you off you chair . . . I got a call from the Cuban ambassador in Mexico City. He wanted me to get a sugar group together to go to Cuba and talk to Castro. I said Castro's not going to want me in there after that tank business. And the ambassador said: 'Fidel knows all about you and the tanks. He likes you because you provided his transportation.'" Favors and Debts

The son of a Pittsburgh meat market owner, Davidson began to piece together his unique web of contacts as an "expediter" for the ammunition program in the War Production Board during World War II, he has said, and "I've been expediting ever since." He has represented the American interests of dictators in Nicaragua ("Somoza called me to get him a 707 out of the country during the Sandinista thing"), Indonesia ("I got Malik to see LBJ during the Commie coup thing when no one else could"); Haiti, and Cuba. He says he's putting together fast food deals in France, import deals in Italy, agritechnology and construction in the Mideast, and expediting ventures for Texas oilman Clint Murchison in Singapore, Malaysia and Indonesia. This year he registered as a foreign agent for Sudan, and is trying to form a lobby-expertise group for the Association of Southeast Asian Nations.

Debts and favors is what it all goes back to . . . the personal level. Irv can get you anything: a hotel room in a crowded city, tickets to a sold-out ballgame, office space, a quick loan. He never forgets who owes him what. When Murchison needed $4 million for a housing project and was too proud to ask his father, Davidson put him in touch with Hoffa on the condition Drew Pearson be allowed to write a column about it. He has been involved in Murchison deals ever since and now Murchison is willing to say about him: "I have found him to be reliable and straightforward and know his other clients have too."

Davidson ran afoul of the law in 1969. At that time he and a friend named Leonard Bursten got an $11 million Teamster Pension fund loan to develop property near Beverly Hills. If his friend Hoffa had still been firmly in control, things might have been different. But with Hoffa out, Davidson and Bursten found themselves pleading guilty to charges of concealing $500,000 in a bankruptcy proceeding when the Teamsters tried to foreclose.

What happened after Davidson's guilty plea is not precisely clear. The record indicates his lawyers moved to have the plea expunged and vacated. The motion, is an unusual turn of events, was granted. Last year Davidson filed a $60 million suit against the Teamsters to recover real estate and damages. 'Re Irving Davidson'

Now part of the Inside Story here, Davidson confides, involves an item in the Justice Department known as the "in-depth file re Irving Davidson." He will make mysterious bits of paper available (who wrote them, where they came from he will not say) describing it as detailing "activities of Irv in the interests of the United States . . . The details are of a sensitive nature. . . ."

"I told those FBI people not to play superagent with me," he says now. "I travel on two passports, but I've never taken a nickel from Uncle for my services. Look at my diary here: Jan. 4, National Security Council. Do you think I planted that? I tell you that I'm dealing day and night with those boys."

He is asked for official corroboration.

"Are you kidding. If those details came out, I'd be useless. Nobody'd trust me."

After some hemming and hawing, a short, smiling State Department man does show up in the office, on the strict condition his name not be used. "Sometimes the interests of the United States requires certain things which because of their shaky nature can not be identified with the United States," he says.

And, with the caution of a true, tried diplomat, that is about as far as he will go.

It is certainly not as far as Davidson himself went in defending his friend Jimmy Hoffa when Hoffa was in trouble. He peddled tapes purporting to tell "explicitly" how a certain Marie Monday had compromised the trial judge (the judge denied it and Monday recanted). He filed an affidavit with the Supreme Court on the tapping of Hoffa's phone. And he lobbied mightily with the Justice Department, where he was seen as "this little guy who used to keep trying to tell Bobby Kennedy what a great guy Jimmy Hoffa was. I mean you had to admire him, you know, in those days it wasn't the greatest thing in the world to be in favor of Hoffa. But he never wavered. Hoffa was a standup guy, he'd say. It's the people around him who are leading him astray."