Some federal agencies, hit with a surprise 16 percent money cut, are making plans to order what could turn out to be massive layoffs starting next month and to furlough workers for short periods to save money.

A number of federal operations are in a Catch-22 situation in that they literally cannot afford to fire people to comply with cuts imposed on them for this fiscal year without, in some cases, practically going out of business completely.

Some agencies are facing cutbacks of up to 25 percent in personnel. The Merit Systems Protection Board, for example, expects to be hit at least that hard even though it is scheduled to hear dismissal appeals from 11,000 fired air traffic controllers, plus workers RIFfed in other agencies. It already has frozen travel for hearing officers and even has run out of money to pay court reporters to transcribe proceedings of cases.

The continuing resolution -- passed by Congress last week and designed to keep agencies without budgets operating through March 31 -- contained language that may require many units, including the White House and the Internal Revenue Service, to make 16 percent cuts in salaries and expense funds. The Federal Election Commission, Federal Labor Relations Authority, Office of Personnel Management, Bureau of the Public Debt, General Services Administration and other agencies are also facing major personnel reductions.

The possible bloodletting arises from Congress' failure to approve agency budgets (for the fiscal year that started Oct. 1) on time, and from layers of spending cuts demanded by President Reagan and generally approved by Congress over the past couple of months.

In September, the Senate Appropriations Committee approved Reagan's revised budget calling for a 12 percent cut in most federal agencies outside the Defense Department beginning Oct. 1. But because the budget picture was incomplete (House Democrats balked at many of the cuts), some agencies began making the 12 percent reductions, while others kept spending at pre-cut levels awaiting final action. That action came Friday when Congress approved a "compromise" resolution that in fact requires a 4 percent cut this fiscal year ON TOP OF the 12 percent reduction for some agencies.

The result is that many agencies without authority to spend at higher levels will be required to absorb the 12 percent plus the 4 percent cutbacks between now and Sept. 30. Many will seek relief, but for now, the personnel picture is grim indeed. Examples:

* GSA has alerted key officials to brace for a possible 16 percent cut in personnel that includes every unit but the Inspector General's office.

* Treasury's Bureau of Government Financial Operations may have to make a cut of as much as 32 percent unless it gets budget relief through the regular appropriation process.

* IRS faces a 16 percent cut in its salaries and expenses account, the fund used to pay employes.

* Some agencies -- because of the heavy first-year costs of firing people -- say they cannot afford to run a RIF and fire large numbers of workers. RIFfed employes get severance pay (of up to one year of salary). Their unemployment benefits also are charged to their agency budget.

* Agencies that cannot afford to run RIFs, or who want to soften their impact -- Federal Labor Relations Authority and others -- are considering one-day-per-week furloughs for an indefinite period. Employes could not -- once a furlough is ordered -- substitute paid vacation for a furlough.

* Because of new budget revisions, Labor Department's Employment Standards Administration, which had anticipated RIFfing up to 300 people, now estimates 1,000 may have to be let go.

* Transportation (outside the FAA), Interior and others are facing personnel cuts ranging from 12 percent to 20 percent.

Hard figures will not be available until agencies get specific allocations from the Office of Management and Budget.