The top officials of the D.C. public school system went to Congress yesterday to say the city's schools are strapped for funds but that they will manage somehow within the budget recommended by the D.C. City Council and Mayor Marion Barry.

School Superintendent Floretta D. McKenzie and Board of Education President David H. Eaton made it clear that they would have preferred a higher funding level in the budget but that they would not try to sidestep the city government by asking Congress to add funds for them.

They presented their views and a justification of the proposed school funding at the third day of hearings on the city's fiscal 1984 budget in the Senate Appropriations subcommittee on the District of Columbia.

The subcommittee also heard from the city's housing director and fire chief on their proposed budgets. The city-approved budget must go through Congress, which can amend it before passing it.

Subcommittee Chairman Arlen Specter (R-Pa.), for the third day in a row the only one of the five-member subcommittee to attend the hearings, asked McKenzie to contact officials at the Lorton prison facilities to see if something could be done about education programs at the youth center there.

D.C. Corrections Department officials had testified Wednesday that there is a 45-day waiting period for educational programs at the facility.

"I am concerned that we are releasing functional illiterates with no trade or skill" from the prison, Specter said, adding that he planned to visit the facility soon.

Housing Director James Clay testified that he did not expect to see any significant reduction this year in the city's waiting list for public housing, now numbering 8,500 families. The city has 12,000 units of public housing, he said, and the city must rely on restoring vacant units to get more families into housing.

Fire Chief Theodore Coleman said that the number of fires in D.C. has declined dramatically from 9,790 in 1974 to 6,353 in 1982 but that fire loss over the same period has risen from $6.3 million to $14.1 million.

He told Specter he was "very much satisfied" with his fiscal 1984 budget.