Even before his agency has finished cleaning out this year's backlog of overdue tax returns, Internal Revenue Service Commissioner Roscoe L. Egger Jr. is promising that next year will be better.

In a recent speech, Egger said steps are being taken to ensure that returns will be processed faster in 1986. The service will place more emphasis on training employes to use the new, $103 million computer system that was responsible for the slowest refund rate in recent years.

"You can't just plug a new system in and expect it to work," Egger told a convention of high-tech executives.

As of July 26, more than 200,000 taxpayers who filed returns by the April 15 deadline still hadn't received their refunds.

So far, the IRS has paid $22.9 million in interest on 1,549,000 late refunds.

Egger also told the Associated Press that he wants to place less emphasis on auditing and more on improving relations with taxpayers. Auditing "is no longer our first priority," Egger said.

"It's taxpayer service. To the extent additional monies come in, unless I'm precluded by law from doing so, it's going to be spent where our problems are greatest."

ON THE MONEY FRONT . . . Whether the IRS will get those additional funds is an open question. Congress recessed for the summer without completing action on the IRS appropriation, and the House and Senate versions differ significantly.

The House version of the bill, which includes funds for the Treasury Department and Postal Service, provides $178 million more for the IRS than the administration request of about $3.5 billion. It would add 2,243 more employes and pay for additional computer equipment to handle taxpayer returns.

The Senate version, which so far has only been approved by the Appropriations Committee, would provide $57 million less than the administration's budget request for new positions and equipment.

The differences will have to be reconciled when Congress returns after Labor Day.

RETURN-FREE FILING . . . Even more money will be needed if the IRS implements the return-free filing system proposed as part of President Reagan's tax overhaul, according to a new report by the Joint Committee on Taxation.

The agency would need "significant additional computer capacity" to be able to process W-2 withholding-tax statements in time to tell taxpayers how much they owe by April 15 and get the refunds out shortly afterward.

The faster this is done, the more taxpayers are likely to participate in the system, the report said. The more people who volunteer, the lower the per-person cost of the additional equipment. As a result, the return-free system, which will be available only to those who don't itemize deductions or use most other tax preferences, is probably only cost-effective under a simplified tax system, the report said.

MORE FURY FROM PHILLY . . . A curious fuss has developed between the IRS and Sen. John Heinz (R-Pa.). Heinz, who has seen his constituents driven crazy waiting for tax refunds from the IRS' troubled Philadelphia service center, has accused the agency of intentionally predating refund checks to save money on the interest it has to pay on late refunds.

His evidence consists principally of one Pennsylvania accountant who says one of his clients received a check dated May 30 on June 10. Because IRS mailings carry no postmark, it's impossible to tell when checks were mailed. The IRS denies any intentional predating.

Heinz, who believed that the IRS was not responding quickly enough to his requests for information, asked the U.S. attorney for eastern Pennsylvania to look into the situation. But his request was delegated -- to the inspector general of the IRS. The report is due this week.