Dwight Ink once delivered a speech to a crowd in Omaha by telephone, from a borrowed airline office, after his plane was grounded by fog in Chicago. As he hammered home his earnest message, his long-distance audience suddenly heard strange sounds over the public address system.

They were the sloshing of a mop and the stern warning of a cleaning woman telling him he'd better climb onto the desk if he didn't want his shoes mopped.

Ink kept talking as he complied, so the story goes, as intent as the scrubwoman on finishing the task at hand.

This juggernaut of a bureaucrat is the man President Reagan hired for the thankless task of making the federal anti-poverty agency disappear. In 30 years in the classic role of the civil servant, facilitator of the policy of the moment, he has dodged mops and has served and survived under seven presidents.

He has run programs ranging from atomic energy through housing through the budget to cleaning up after an earthquake in Alaska.

In an era dominated by charges that the bureaucracy is hard to move, Ink scoffs at red tape.

"I regret the notion that the bureaucracy is non-responsive," he said, blinking behind his thick spectacles, a man about as flashy as a filing cabinet, and as shakable.

"The problem is that we don't do a good job of providing good leadership. The bureaucracy does respond to good leadership at the top-management level. They have to know what's expected. I think they are responding now, here, in most difficult circumstances."

He said he believes that good public servants carry out the policies of elected leaders, but he said he also believes that good leaders must trust and rely on their career employes to help determine that policy. Too many administrators, he said, mistake candid recommendations or objections, made by their career staf-fers, for disloyalty.

One of Ink's talents is that, like Lamont Cranston, "The Shadow" on the old radio show, "he has the ability to cloud men's minds," according to one veteran government-watcher. "He can talk that bureaucratic lingo, and make it sound like he's really said something. Everybody says, 'Wow.' I don't know how he does it."

Ink now bears the soon-to-be obsolete title of director of the Community Services Administration (CSA), what's left of the Office of Economic Opportunity, created in 1964 to wage Lyndon B. Johnson's War on Poverty. The agency has been ordered to self-destruct by Oct. 1 and scatter its authority to the states. Other agencies may soon follow the kamikaze blueprint Ink is designing for this one.

Ink is known to colleagues as a skilled administrator who can play the bureaucratic levers like a virtuoso, make a call at the right moment, cultivate a member of Congress and build crucial relationships between the permanent career employes and the shifting surface crust of political appointees.

Even the employes whose jobs he is canceling methodically don't seem to resent him. "I believe he is a good administrator, a decent individual," said David Matthews, a veteran anti-poverty employe and an officer in his union local, a unit of the American Federation of Government Employes, which has taken legal action to try to save the employes' jobs. "But his hands are tied by the administration, which is carrying this out in the harshest, most precipitous way they can."

To those who criticize his current project as a desertion of the poor by the government, Ink emphasizes that he believes the programs will continue, just in different hands. A primary architect of the "new federalism" of the Nixon administration, he said he believes that any program can be better managed by people "out there," close to the problems.

"I do not accept the idea that the federal government is highly efficient and the states are inefficient, that people at the federal level are highly compassionate and the states ignore people and social problems . . . ," he said.

Like many veterans of federal service, Ink argues that the government places too little emphasis on management skills and is driving out its best management talent through a false economy, failing to provide economic and other incentives for them to stay. The problem is compounded, he adds, by generous government incentives to retire early.

He blames many of the problems of the CSA, long a favorite whipping boy of Congress, on deficiencies in this area. "I admire many of the career people. But they've been handicapped by political leadership that has often been indifferent to, and sometimes intolerant of, good management," he said.

Ink began his career as an assistant city manager in Fargo, N.D. There, just over a year out of college, he resigned to protest the firing of the city manager when the manager tried to expose local corruption.

Ink has been a top manager at the U.S. Atomic Energy Commission, the Housing and Urban Development Department, the General Services Administration and the Office of Management and Budget. President Johnson sent him to Alaska to direct the restoration of services after the earthquake of 1964. Now retired from the career service, he left a vice presidency of the National Consumer Cooperative Bank to take his current assigment.

Where will he go after Sept. 30, when the doors are to close on the CSA? "I have no idea," he said. "But I've been out of work before."