By all conventional standards, this state's New Right conservative Sen. Roger Jepsen should be politically dead. Few politicians in Iowa history have found themselves in so many embarrassing situations. Few have seemed so bumbling.

But Jepsen, considered the most vulnerable of all Republican senators even before a flap over a 1977 visit to an X-rated health spa, has risen from the political grave and now is given a 50-50 chance to win reelection to a second term.

He has done so by turning publicity over the visit to the spa into an unlikely political plus and beating to the punch his Democratic opponent, Rep. Thomas R. Harkin, in a vicious round of name-calling and negative advertising.

He has accused Harkin of being a "big-spending liberal" and practitioner of "false-front techniques" who has often failed to vote Iowa's interests in Congress. Harkin has supported legislation to protect the auto industry from foreign competition. Jepsen said his rival would rather "fatten the bank accounts of Detroit auto makers" than help Iowa farmers, who might lose export sales in a trade war.

Jepsen also has suggested that Harkin has liberal friends who don't believe in such basic Midwestern institutions as land-grant colleges, hot dogs and 4H clubs, and he has told Iowans that Democratic presidential candidate Walter F. Mondale "refuses to eat red meat," raising "serious questions about how faithfully he would represent the farm state of Iowa." Mondale, who made the advertising phrase "Where's the beef?" famous, eats red meat regularly and is a particular fan of cheeseburgers.

Harkin, 44, a five-term congressman, has replied in kind. And this race has degenerated into a messy if not downright silly personality contest that blurs the stark ideological differences between the two candidates.

Harkin has called Jepsen "Red Ink Roger," a man who "parades as a conservative" but is "the biggest spending senator in Iowa history." His television commercials mock Jepsen.

"When two Iowa farmers drove a tractor all the way to Washington to talk to him about farm debt, Roger Jepsen fell asleep," says an ad that features a hog snorting loudly.

Then, there is the "war-record" issue.

After Harkin was quoted as saying he flew "combat air patrols" in Vietnam, Sen. Barry Goldwater (R-Ariz.) came to Iowa and accused him of fabricating a combat record. Harkin, Goldwater added, represented "the greatest danger to American security in history." Harkin, a former Navy pilot, acknowledged that he really flew planes from Vietnam to Japan for repairs.

Jepsen, 55, also developed war record problems. It was revealed that he once claimed to be a World War II paratrooper, although he didn't enter the service until 1946, a year after the war ended. He said he used that description because the Veterans Administration considers that the war "technically ended in 1946."

With the election three weeks off, there is no end to this high-mindedness in sight.

"It works. It works," said Harkin's media advisor, Bob Dow. "We came on the air two, 2 1/2 weeks after Jepsen did with the hard negative stuff. In the meantime, we lost and lost big."

This is dramatically illustrated in the Des Moines Sunday Register's Iowa Poll. After running as many as 17 percentage points behind Harkin, Jepsen moved nine points ahead of him in late September as his negative ads hit the airways. Harkin then launched a negative ad campaign of his own, and a poll conducted last week found that he had recovered and was 5 points ahead of Jepsen again.

That Jepsen, the Lazarus of Iowa politics, is even in the race is one of the miracles of the election season.

His misadventures in Washington were almost legendary even before two Iowa radio stations reported last June that he had signed an application for membership in Leisure Spa, Ltd., featuring "nude encounters and nude rap sessions."

He had, for example, been called "the senator for sea turtles" for championing a Grand Cayman Island turtle farm, and raised the wrath of Washington commuters by claiming congressional immunity when stopped by police driving alone in a car pool lane.

"It's perfectly legal," he said. "I drive my American-made car to work as provided for in the Constitution."

His use of office staff and campaign funds also came under question.

And a White House official had boasted "we just beat his brains out" to get Jepsen to reverse himself in a sensitive 1981 vote on the sale of AWACS radar plans to Saudi Arabia.

Jepsen, the chief sponsor of the Family Protection Act and a leading advocate of New Right conservative social values, turned the health club incident, which occured before he became a senator, to his advantage first by claiming that he didn't know what went on in the club and then pleading for forgiveness as a "born-again" Christian who had seen the error of his ways.

"I have been stripped of all worldly pride and humbled before the entire nation," he told the annual state GOP convention. Sympathy built for him as he campaigned across the state with his wife, Dee, and his mother at his side.

"Iowans are strange people. Every one of us at some point has done something that wasn't quite right. We've gone to a girlie show at the county fair or shot a pheasant out of season," said Bernard Ebbing, Jepsen's Black Hawk County chairman. "We know Roger shouldn't have done what he did, but we don't crucify people for being human."

Jepsen, now running his eighth statewide race, also has benefited by closely attaching himself to President Reagan, once a sports announcer in Des Moines. Reagan, Vice President Bush, two Cabinet members and 14 Republican senators have come to Iowa to campaign for him.

Democrats complain that Harkin, who has not run for statewide office before, sat comfortably on his lead too long without capitalizing enough on Jepsen's misfortunes.

But his campaign slogan is a reminder nevertheless. "A senator Iowans can be proud of." That is what the voters are urged to choose next month.