An explosion of tax shelters, tax protestors and tax evaders in the "underground" economy, combined with massive backlogs of paperwork, has placed the nation's tax system under "significant strain" and is costing the government tens of billions of dollars in lost revenue, the Internal Revenue Service commissioner said yesterday.

Roscoe L. Egger Jr., in a speech to tax lawyers meeting here at the annual convention of the American Bar Association, said that personnel shortages and repeated changes in the tax laws since 1976, the most recent just last week, have contributed to the problem.

While taking care not to part from the administration's position on the tax cut bill, he said a lot of other work will have to be put aside to implement the changes.

He described the impact of the agency's problems in the billions. The backlog of unprocessed appeals by taxpayers now totals $1.4 billion, compared with a $7.2 billion backlog in 1977, he said. Twenty percent of those involce tax shelter schemes challenged by the agency. The agency expects 500,000 cases of "tax protest" over the next year, ranging from fradulent withholding attempts to phony tax exemption schemes.

The IRS faces 3.6 million deliquent tax accounts at the moment, he said. Within a few years it expect to list $6.5 billion in "accounts receivable" from such deliquencies.

It is also losing an estimated $23 billion to the so-called "underground economy" of people, such as waiters, housekeepers and cabbies, collecting cash for their service and paying virtually no taxes.

Egger called the tax shelter situation the "most pressing problem." He said it had become "America's fastest growing industry." Egger said in an interview later that he had targeted his pointed comments at this group, the lawyers who designed the shelters: certain commodity, real estate and other investments designed exclusively to enable a taxpayer to avoid taxes through deductions. The lawyers received his remarks with polite applause, but passed up Egger's inviation to ask him questions or challenge him.

Egger said in his speech that the IRS is now challenging about 230,000 tax shelter cases. He said that two of the most popular commodity investments are manipulative commodity investments and a well-publicized Bibly-buying scheme.

The Bible controversy, Egger explained afterwards, involves the wholesale purchase of Bibles, their subsequent overvaluation by the purchaser, their donation to a church institution and finally their deduction at the overvalued rate as a charitable contribution.

"As these shelters proliferate," he told the tax lawyers, "confidence in our system decreases. More and moe, we are hearing that the wealthy and the rich are not paying their share . . . the system has a severe image problem."

Egger also attacked the increasing number of "tax protestors." He included among this group the tens of thousands who have recently tried to avoid weekly withholding deductions by the IRS by declaring many more personal exemptions on withholding forms than they really have.

He also said that uncounted thousands were purchasing religious ordinations from the Universal Life Church, contributing money to themselves and treating it all as a tax-exempt religious enterprise.

Collectively "they're flooding our courts with frivolous cases."

Egger said that inflation had contributed significantly to the agency's collection problems by rendering businesses unable to keep up with their tax payments.

The agency's work force has grown only 2.3 percent since 1977, he said, while the work load has risen by 10 percent.

Egger said the agency was still behind in writing regulations to implement five major pieces of tax legislations since 1976.

"And then, of course, along come the 1981 economic recovery act," Pesident Reagan's tax bill. Egger said the bill would substantially help in closing off some of the tax shelters and in solving other problems.

But it will create a new onslaught of work for the understaffed IRS, he said.