As April approaches, the man Americans may be thinking about most - often with a vengeance - is Jerome Kurtz. Kurtz' name admittedly isn't a hosehold word in most communities, but his job is. The former Philadelphia tax lawyer is U.S. commissioner of internal revenue. Since early last May, his name has been on all IRS orders and instructions - including the tax returns due April 17.

Like most IRS commissioners, Kurtz has kept a low profile since he took office last May, replacing Nixon appointee Donald C. Alexander, who has returned to private practice. Kurtz has made relatively few speeches - mostly to accountants' groups - has avoided news conferences, and seldom appears at public gatherings, except to testify before Congress.

But the consensus is, that within the confines of the IRS job, Jerry Kurtz may be one of the Carter administration's best and brightest appointments. In 10 months in office, he has restored order and morale to the badly battered IRS bureaucracy, has mounted an aggressive attack on tax-shelter abuses, has trimmed the backlog of tax rulings and has simplified income tax forms somewhat.

Moreover, he has managed to retain the respect of both liberals and conservatives. Robert M. Brandon, director of Ralph Nader's tax reform lobby group, praises Kurtz for being "willing to take some fresh approaches on things." And although conservatives aren't enthusiastic about Kurtz' crackdowns on tax shelters, they at least credit him with being "reasonable."

Among Kurtz' accomplishments:

A series of first-step crackdowns - some successful, some not - against major tax-shelter abuses and business misuse of travel and entertainment deductions. Kurtz first ordered a stepup in audits of tax-shelter ventures and then proposed new rules and legislation to make it easier for the IRS to flag violations. He also has proposed taxing fringe benefits as ordinary income.

A major improvement in morale at the 88,000-person agency. Although Kurtz' predecessor, Alexander, was a knowledgeable and well-intentioned commissioner, insiders say he often was abrasive in handling subordinates and tried to make too many routine decisions himself. (One aide complained that Alexander's office was so laden with papers there was nowhere to sit.)

Kurtz immediately changed all that by delegating most decisions to his assistant commissioners and their staffs, reserving to himself only those involving major policy changes. His desk, by most government standards, still is cluttered. But there's no spillover onto chairs and worktables. And the IRS bureaucracy is functioning more smoothly.

Continuing the "opening up" of IRS' previously vest-tight public disclosure policies. The agency now makes public all rulings it provides companies on specific tax issues - once revealed only to the firms involved - and generally makes more information available to the public than it used to. Alexander began the shift, but insiders say Kurtz has changed agency attitudes.

A visible streamlining of the IRS' long-undecipherable 1040 and 1040A forms for individual tax returns. Under Kurtz' orders, IRS redesigned the forms last summer to make them easier to read and run the computation in order from front to back. The result: a dramatic drop in taxpayer error rates, at least according to initial reports from field offices.

The agency also has improved its program to help taxpayers fill out returns - although a study by the General Accounting Office last week showed that IRS taxpayer-assistance personnel answering inquiries over the phone had only a 79 percent accuracy rate when the questions were of any complexity. Kurtz has pledged to work on the problem further.

Admittedly, not all of Kurtz' efforts have been smashing successes. Critics point out the commissioner has had to soften his stand somewhat on issues that sparked controversy - such as his fringe-benefits rulings and proposals involving recordkeeping for travel and entertainment expenses and for tax-shelter partnerships. And some onlookers argue his impact hasn't been all that visible outside the agency's national office.

Kurtz has had to postpone a 1977 attempt to require taxpayers to "flag" their returns when they've taken deductions that the government might find questionable. And he's "modified" - by paring back - a plan Alexander began to require corporate officers to answer advance questions on returns about possible slush-fund payments.

Perhaps most tellingly, Kurtz' plan to tax fringe benfits has run into substantial opposition in Congress. The House Ways and Means Committee voted last year to bar the IRS from issuing fringe-benefit regulations until Congress has had a chance to review them. The commissioner says he'll try again next summer to draft tentative regs - but no one is holding his or her breath.

And Kurtz still has a problem with disgruntled members of the IRS' crack "intelligence divison" - the T-man-style supercops who traditionally have teamed with FBI and drug-enforcement officials in interagency strike forces. The raids were cut back during Alexander's administration, largely to offset anti-Nixon reaction. But the gung-ho agents never forgot.

The new commissioner hasn't changed Alexander's approach. The intelligence division still is being kept at what Kurtz calls "minimal level," with joint FBI and drug raids confined to cases where a tax violation is suspected. But Kurtz aides say the IRS chief plans to take other measures to improve morale among the special agents, by showing personal support.

In fairness, some of what Kurtz has put into force is mainly an extension of what Alexander began, but never quite put into action. Says Albert B. Ellentuck, Washington tax specialist for the accounting firm of Laventhol and Horwath: "Alexander mostly did a lot of warning. But Jerry Kurtz is going after it."

What seems surprising to some observers is that Kurtz has been able to seem even-handed though his personal philosophy on taxes is so liberal. Underneath the measured phrases of Kurtz' IRS commissioner image beats the heart of an out-and-out "tax reformer" - anathema to most businessmen and politicians. Yet Kurtz hasn't tried to hide it any. He's just careful not to campaign.

An example is in Kurtz' ruling last fall on an issue close to the hearts of "tax reformers" - whether royalty payments by U.S. oil companies to Saudi Arabia should be treated as income taxes (eligible for a big tax credit) or as a business expense, merely qualifying for a deduction. Kurtz took the middle route, denying the oil firms the bigger break, but only on narrow grounds.

Kurtz' link with taxes began when he was a college student. An accounting major as an undergraduate, he found number-juggling boring, decided to try law instead. At Harvard Law School, he discovered the two fields mixed happily. After a stint in the Army, he joined the firm of Wolf, Block, Schorr and Solis-Cohen. With a break for a tour at Treasury, he's been there ever since.

Kurtz' time at Treasury - has was tax legislative counsel in the last two years of the Johnson administration - imbued him with two things: a broadened (and liberal-oriented) approach to tax policy, and a friendship with several key Treasury tax aides who later would take tax policymaking appointments during the Carter administration.

Kurtz was recruited for the IRS post by the Carter administration's first chief tax policymaker, Laurence Woodworth, who died of a stroke last December. Kurtz had been one of a handful of tax lawyers testifying before Congress over the years who believed in tax "reform." (The other was Donald Lubick, now Woodworth's successor. Woodworth hired them both.)

Kurtz now enjoys a close working relationship with Treasury, where he deals mainly with Lubick - a contrast to his predecessor, who reported only to the deputy secretary. (The two men shared bachelor quarters here while their appointments were being processed.) While the administration was shaping its "tax reform" package, Kurtz had informal say beyond the role of commissioner.

His major difference with Treasury officials has been over the timing of the ruling on the Middle East oil royalties question - an issue that ultimately was resolved by outside factors. On the rest of the tax docket, Kurtz and Lubick have a simple arrangement: Lubick gets his way on policy, and Kurtz on matters affecting administration.

So far, both say, there've been few clashes. As Kurtz says sardonically of his late-1960s experience at Treasury: "It gave me more of an appreciation of what was possible."

At the IRS, the new commissioner has made only a handful of personnel changes, leaving Alexander appointed assistants to carry on in their previous jobs. The IRS hierarchy is mostly under the jurisdiction of the Civil Service Commission. Kurtz could have shuffled some to district offices, but chose not to. "I didn't feel I had to make any changes," he says.

An affable and highly articulate man, given to semiconservative suits and expensive dress shirts, Kurtz has an unreformer-like yen for foreign travel and fine food (he's an expert gourmet cook himself, according to friends). His wife, Elaine, is an artist. They have two daughters, both in their late teens.

Kurtz concedes there's still a lot of work to be done at the IRS, first to unclog more of the backlog of unwritten regulations and rulings - the IRS still has more than 350 regulations still to write, some of them stemming from changes enacted in 1954 - and second, to beef up the agency's processing equipment and auditing staffs.

(The IRS sought a sophisticated computer setup to replace outmoded equipment installed in the early 1960s, but ran into opposition from liberals, who feared it would establish a "Big Brother" spy operation. Now the agency simply is replacing its old equipment with comparable models. Kurtz also hopes to change the system to flag more returns involving tax-shelter abuse.)

At least some of what Kurtz has in mind - both for the strike forces and the IRS in general - will take more money. Increasing the amount of IRS auditing, for example, would require a substantial boost in appropriations, which now seems unlikely. And any further push to tax fringe benefits and crack down on tax-shelter abuse could pit Kurtz in a battle with Congress.

Still, for the commissioner's first few months on the job, the assessments seem to be coming in with consistent high marks. And considering the way Washington has received other top Carter administration appointments, that may be a welcome breath of spring air, even at tax time.