There are 15 men and women out there in the federal bureaucracy who could tell President Reagan where a lot of bodies are buried as his administration begins its much-heralded search for waste, fraud and mismanagement in federal programs.

They make up the corps of inspectors general at major federal agencies. But, instead of debriefing them, Reagan fired them all last week.

Inez Smith Reid, the inspector general at the Environmental Protection Agency, for instance, could talk about the $133,000 worth of unused airline tickets dating back to 1972 that she found under a secretary's desk during a recent audit.

Thomas F. McBride, the former Watergate assistant special prosecutor who was inspector general at the Agriculture Department, could detail the widespread use of food stamps as an underground currency to buy drugs, illegal weapons and cars.

June Gibbs Brown, the IG at the Interior Department, might volunteer her discovery that a youth camp director in Missouri ordered 1,072 pairs of leg chaps, 3,736 pairs of work gloves, 112 stepladders and 1,509 desk calendars, all for a camp that was scheduled to enroll 136 youngsters.

The IG's tales of waste and fraud range from the trivial to the enormous, from the Energy Department employe who was caught running up $100 in long-distance telephone bills between his office and a pornographic story "hotline" in the Midwest to the mortgage bankers in Puerto Rico who set up phony housing sales to siphon off millions from the Department of Housing and Urban Development.

When Reagan abruptly fired the IGs last week, some Democratic sponsors of the 1978 inspector-general legislation criticized the move as politicizing the fledgling corps. Congress' intent, they said, was to create independent, nompolitical offices in the major executive departments, though the president has right to replace the IGs.

Reagan aides did say the fired inspectors can reapply for their jobs in the new administration if they think they can meet the new president's challenge to rip into waste and fraud like a "junkyard dog." Several IGs are trying to stay on.

During his presidential campaign, Reagan continually declared the elimination of "waste and fraud" a top priority. He tied the success of his entire tax-and-budget-slashing recovery program to finding and cutting tens of billions of dollars in fraud and waste from government programs.

When asked during his televised campaign debate with President Carter how he would cut spending while cutting taxes and increasing the defense budget, Reagan replied, "I believe there is enough extravagance and fat in government."

He cited the Carter Cabinet secretary who once estimated that there was $7 billion of fraud and waste in the Department of Health, Education and Welfare alone, and the General Accounting Office estimate of the "tens of billions of dollars that is lost in fraud alone."

While hard figures on the magnitude of waste and fraud are elusive, several members of the outgoing class of Carter inspectors general agreed in interviews that they barely dented the problem. They also contend that, while fraud is prevalent, mismanagement and inefficiency do the greatest damage to taxpayers' wallets.

Like good bureaucrats, the inspectors say that they would do better if they only had more help, that they don't have enough auditors and investigators to police the multibillion dollar programs. Some say they have been hampered by backbiting in their own offices, lack of support from Cabinet officers, or the difficulty of merging sometimes incompatible audit and investigative staffs.

But their biggest complaint is that program managers in the various agencies aren't held accountable for correcting the problems the IGs uncover.

"Cabinet officers need to start demoting and firing program managers for inattention and negligence to waste and fraud issues," said Agriculture's McBride.

Donald L. Scantlebury, director of the GAO's accounting and financial management division, which investigates waste and fraud for Congress, is sympathetic to the IGs' frustration. "I think the [IG] concept is working out well," he said. "But it's a little early to expect dramatic results."

The idea of putting independent inspectors inside the Cabinet agencies was resisted by the executive branch for years. The first inspector general's office was set up at Agriculture in 1962 after internal audits failed to uncover the schemes of Texas fertilizer swindler Billy Sol Estes. But Agriculture Secretary Earl L. Butz abolished the office during the Nixon administration.

The first statutory inspector general was established after a House investigation found that HEW had only 10 investigators to oversee a $118 billion program. A 1978 law set up IGs in 13 additional agencies. The Department of Energy got an inspector general a year later. Because of hiring freezes, however, only about 5,300 of an authorized 5,900 slots for auditors and investigators have been filled.

The Defense Department, which doesn't have an inspector general, does have 18,000 auditors and investigators to oversee a $185 billion budget. By contrast, the Department of Health and Human Services, HEW's successor, has only about 700 auditors and 100 investigators to watch over a $260 billion budget.

Several of the inspectors general regard the required semiannual report to Congress as their greatest weapon against unrepentent federal program managers. "Without that statute we wouldn't last eight seconds," one out going IG said.

Some of these reports are filled with undecipherable statistics, while others are highly readable chronicles of program abuse. McBride's latest report, for example, tells of two Greenville, S.C., men who sold five cars and trucks, 32 firearms and some marijuana to undercover agents in return for food stamps. In Gary, Ind., the assistant fire chief was convicted of selling $11,000 in food stamps for $7,000 cash to undercover agents from McBride's office.

Paul R. Boucher, IG at the Small Business Administration, said in a report early this year that five farmers who received $1.4 million in SBA disaster aid loans at 3 percent interest diverted some of the funds to 10 percent interest certificates of deposit, and bought stocks and tax-free municipal bonds with more of the funds.

Richard B. Lowe III, who has been acting IG at the gigantic HHS, said he was upset to learn that the Social Security Administration doesn't have adequate controls to prevent employes with access to computers from diverting benefit checks to themselves.

The greatest cheaters, according to the audits, are not individual welfare or health care recipients, but doctors and pharmacists and other providers of services who overbill the government. A recent HHS audit screen detected abuse in laboratories in the Los Angeles area that led to an FBI undercover investigation called "Labscam" and several kickback indictments.

EPA's Reid, with only 95 auditors, has been trying to police the nation's largest publc works project -- the $30 billion sewerage construction effort designed to clean up the nation's rivers -- and she says she loses sleep over the vast areas of EPA operations she couldn't even look at.

"Because of poor management, the federal government is losing millions, perhaps billions of dollars," she said.

When Energy Department inspector general J. Kenneth Mansfield looked into a synfuels pilot plant built by Ashland Oil, he found that firm had put up a $1 million brick administration building instead of the prefabricated model called for by DOE. As it happened, the elaborate new building was adjacent to an Ashland refinery.

Too late to recover the government's loss Mansfield called for sweeping management changes on the project, some of which were adopted.

Several of the outgoing IGs voiced the concern that Reagan's pledge to cut billions in waste will fall on its face unless their successors get more help.

To put a serious dent in waste, they said, the president will have to increase support for the program, especially within the Office of Management and Budget and in some agencies where sub-Cabinet administrators have starved the inspectors' budgets, cut travel funds to do audits, refused to place all uditors directly under the control of the inspectors and, in some cases, attempted to head off investigations.

"I personally would not want to continue [in the job] without a commitment that the agency wanted this kind of work done or that they intended to support it," said Interior's Brown. She said she found then-Secretary Cecil D. Andrus a pleasure to work for, but he was seldom there to back her up when program chiefs ignored her audit findings or refused to recoup challenged expenditures.

Reid said that then-EPA Administrator Douglas Costle never returned her memos. "To this day I don't know what his feeling was about the program," she said.

The day after the Energy Department's Mansfield released a report critical of a top aide to former Energy Secretary Charles W. Duncan Jr., Duncan called the surprised inspector into his office and asked him to consider a job in Paris, even though the department had no office there.

Most of the fired inspectors have been on the job less than two years, and some of them said they were deeply wounded by Reagan's action.

"I really like my job and want to keep it," said former prosecutor Roucher at SBA, who in the waning hours of the Carter administration blew the whistle on a presidential assistant who got Carter to sign an order quadrupling the size of a minority and program even though Congress had forbidden it.

A career man in Carter's Senior Executive Service, Boucher sent in his reapplication for the job to Reagan Thursday.

One inspector general summed up his view of Reagan's firing this way:

"Everybody wants a strong IG operation until it starts investigating them. The administration may start out thinking they want junkyard dogs, and what they may end up getting is French poodles."