For taxpayers, April 16 spells relief. Officially, it's The Day After. Overnight, America's most menacing deadline is yesterday. But for a growing number of taxpayers each year, the worst is yet to come.

When Efren Herrera mailed a petition to the Internal Revenue Service from Dallas, he sent it by certified mail just before the deadline. The stamp fell off en route and the envelope was returned to him for postage due. Frantically, Herrera remailed it. Too late. The IRS' response: Tough.

Herrera decided to take on the IRS, joining approximately 42,000 other Americans who last year (up from 17,000 in 1979) defied intimidation and odds to take their complaints to U.S. Tax Court. For many, it would be the closest they'd ever come to fighting City Hall. Most found out you can't.

Statistics from the 1984 IRS Commissioner's Report show the government's edge: Of the tax cases settled last year in U.S. Claims, District and Tax courts, the IRS won 56.8 percent, taxpayers won 6.7 percent and 35.5 percent represented partial victories for both. In the courts of appeal, the IRS won 82.8 percent, taxpayers won 10.6 percent and victory was split in 6.6 percent of the cases.

But despite the overwhelming odds, tax experts say you have a chance of beating the IRS -- if you're gutsy and have a valid complaint.

In Herrera's case, the Tax Court decided that under the circumstances "only a magician" could have met the due date, adding it was the Post Office's fault, not the taxpayer's. Ruling: The IRS must accept the petition as "on time."

"Most of the time the IRS wins," concedes Jeff Schnepper, associate professor of Taxation, Accounting and Finance at The American College, Bryn Mawr, Pa., and author of How to Pay Zero Taxes (Addison Wesley, $8.95). "The poor average taxpayer doesn't know the law; but neither, frankly, does the average IRS agent."

In 1981, says Schnepper, the U.S. General Accounting Office (GAO) checked a sample of 2,543 individual income-tax returns in which the IRS had found 3,720 errors in arithmetic. GAO discovered nearly two-thirds of the errors were made by the IRS. Of the 33 million errors found on 94 million individual income-tax returns processed in 1981, the GAO claims 63 percent were made by the IRS.

But fear of God and the IRS seems comparable at tax time. In court, that works in the service's favor, says Schnepper, a practicing tax attorney in New Jersey who likes to cite English poet Robert Herrick's admonition of Charles I: "Kings ought to shear, not skin, their sheep."

The complexity of tax laws, claims Schnepper, snubs out countless bona fide complaints, while frivolous court battles and shady claims only add to the IRS' image of invincibility.

"I've got a letter from the IRS that reads: 'Dear Taxpayer. We have misplaced your file. Unless we find it within 30 days, you will be subject to a five-year imprisonment and a $10,000 fine.' It's a phony, of course, but the paranoia it suggests is real. The average Joe out there doesn't know the law. When the IRS says, 'Whoa, fella, this is it, this is the law, pay up,' most people do."

Although he admits the IRS is tough to beat, Jack Warren Wade Jr. says the odds are better than they appear. The former IRS revenue officer and author of When You Owe the IRS (Penguin Books, $6.95) claims the service's compulsion to win its cases can benefit the litigious taxpayer.

"The IRS likes to be able to boast that it has an extremely high success rate," says Wade. "They want to win it hands down once the case goes to court -- because that's intimidating.

"I advise people that if they think they have a legit case, take it at least to the appeals level. The IRS doesn't like to lose. If they feel they're going to lose, they'll give it up and settle with the taxpayer at that level." (In 1983, adds Schnepper, 84.1 percent of the cases taken to the appellate level of the Tax Courts were settled by aggreement.)

"You've got to beat them inside the system," says Wade, "playing their game. And you've got to have a bona fide claim."

For inspiration on this hand-wringing day, here are some cases from court records of taxpayers who did -- and won:

* Corporate executive Lester Crancer thought of Cathy Austin as more than just his secretary. In exchange for her vow that she wouldn't marry anyone else, he gave her several thousand dollars, a house and promised her a share in the company. Crancer died before he could make good on the stock promise and Austin sued his estate to collect.

* IRS: Austin owed income tax on the house, cash and stock she received.

* Tax Court: The house and cash were tax-free gifts, but the stocks were compensation for services provided by Austin as Lester's companion, and therefore taxable.

* The IRS penalized Robert Ferry, a retired Air Force pilot in Lake San Marcos, Calif., for taking a fat deduction on an illegal tax shelter investment. It claimed he knew the transaction was a questionable scheme to evade taxes when he handed over $32,000 to International Dynamics, which promised to return 90 percent of the "investment" a month later as tax-free gifts.

Tax Court: Ferry hadn't evaluated the investment himself but had relied on the advice of his accountant, who thought the investment was legit. No penalty. When Clayton Graham of Barrington Hills, Ill., planned his new house, he hired a contractor to build it to his specifications -- requiring the contractor to keep records of all sale taxes paid on building materials. Graham deducted about $6,000 in related sales taxes on his Schedule A.

IRS: Graham can't deduct the taxes of construction supplies because the builder paid for them.

* Tax Court: Graham closely oversaw all building and, therefore, incurred the sales taxes. They're deductible.

* Three taxpayers refused to comply with an IRS summons demanding they hand over documents and testify in a tax case involving another person. They knew the documents and testimony would prove that they received income they failed to report on their income-tax returns.

Circuit Court Ruling: The summons violated their rights against self-incrimination under the Fifth Amendment. Two IRS agents grabbed the assets of a Pennsylvania horse breeder under the false assumption that she was hiding taxable funds for her boyfriend, who was the focus of their investigation. A U.S. District judge ruled their actions had "no reasonable basis," had violated the woman's Fourth and Fifth Amendment rights, and found the agents personally liable for $67,000 in damages.

* Walt Eller hired his children, ages 7, 11 and 12, to help part-time in cleaning up the trailer park he operated. He deducted the wages he paid them, including $1,200 the 7-year-old earned, on his income-tax return. The IRS said no.

Tax Court: Reasonable compensation to your children for real work is a deductible business expense.

* A San Jose, Calif., insurance salesman's home was his office, so he reported $11,000 in business expenses on his income-tax return. The IRS allowed his deduction of travel expenses from one client to another, but not travel from his home to his clients.

Tax Court: The salesman's home qualified as a place of business, making deductible his business-related travel costs beyond his "commute" from his bedroom to his home office.

* A couple who had income from illegal sources filed a tax return reporting their income, but not how they earned it. They claimed Fifth Amendment privilege against self-incrimination and the IRS claimed the couple had not filed a completed return.

Tax Court: The return was valid because there was enough information to determine the tax owed.

* A Florida court threw out an IRS summons demanding Wayne La Mura's telephone and banking records to investigate his charity contribution deductions, calling the request excessive.