John Oller’s new book tells how the FBI took down John Dillinger, Baby Face Nelson, Bonnie and Clyde and other celebrity criminals of the 1930s, as President Franklin Delano Roosevelt waged his “war on crime”. In prose fast as an Essex-Terraplane getaway car, Oller recounts and deconstructs the myths that grew around such bank robbers, kidnappers and killers. He also spotlights the agents who chased and caught and sometimes killed the criminals or were killed themselves – names long eclipsed by that of J Edgar Hoover, who led the FBI for 48 years.

“Hoover was such a larger-than-life figure and he wanted to keep it that way,” Oller says. “He wanted his agents to be anonymous. If any name was going to be associated with the FBI, he was going to be it. And he pulled it off. That’s the reason none of these guys that I write about have ever been known. They kept it that way.”

Like the criminals they hunted, agents (“G-Men” in the slang of the day) have occasionally been played by Hollywood stars: “In the movie Public Enemies with Johnny Depp as Dillinger, Christian Bale played [Hoover’s deputy] Melvin Purvis. It was total miscasting. But none of the other guys in my book are really known to the public. Sam Cowley [who killed Baby Face Nelson but was killed himself, in 1934] may be known a little bit, if you’re really versed in the genre.

“So I was attracted by the anonymity of these guys [and] I wanted to bring to the fore some of these people who had never been talked about … I wanted to track down the descendants.”

Oller did so, talking to sons and daughters, grandsons and granddaughters. If the result is a little more public interest in Walter F Trainor, who unraveled the conspiracy behind the Kansas City Massacre, or Johnny Madala from Chicago, or Bill Rorer, who captured Machine Gun Kelly (the kidnapper, not the rapper), then to Oller, so much the better.

Oller is well aware the FBI’s reputation has never been spotless, though he does laugh at how distrust of the “Feds” has recently switched from left to right. Of Hoover, who died in 1972, Oller says he “takes a lot of criticism, some of it very justified”. Much of it comes from the 1950s and 1960s, when as the Guardian recently put it, Hoover pursued “strong-arm tactics, political manipulation and disregard for civil liberties, [using] the FBI’s extensive intelligence-gathering capabilities to monitor political dissidents, civil rights leaders and other groups he deemed a threat to national security”.

Looking back to the 30s, when Hoover sent agents chasing across state lines, Oller says: “One of the things a lot of critics say as well is, ‘Why did he spend all his time going after these two-bit bank robbers instead of the mafia, organized crime?’ The mafia, it was mostly a big-city phenomenon. They dealt in big-profit items: counterfeiting, prostitution, gambling, alcohol, drugs and the like. Whereas these guys” – Dillinger, Nelson et al – “were bank robbers and with some of these midwest banks they were taking a flyer, really.”

It was the time of the dust bowl and the Great Depression.

“How much money would be in the bank? Sometimes the robbers were told, ‘Oh, there’s $200,000,’ and they get there and there was only $15,000 because the bank had just deposited its money in the Federal Reserve. But while bank robbery was fairly easy to succeed at, you had to be willing to shoot people, if necessary. There was killing of cops and innocent bystanders.

“So I say in the book, it was true: if you were a Main Street shopkeeper or small-town cop or an innocent bystander on the street, you’re in much greater danger of being killed or seriously wounded by a John Dillinger or a Bonnie and Clyde than you were by Al Capone in Chicago. The mafia, big organized crime, they might go after each other at times, and they might go after the cops if they hadn’t paid them off sufficiently. But for the most part, it was the scourge of these bank robbers that got the FBI involved, and the kidnappings too.”

Gangster Hunters opens with a kidnapping, of the baby son of Charles Lindbergh, the aviation hero, in New Jersey in 1932. “The crime of the century” transfixed a nation. But Oller also recounts kidnappings of businessmen, among them the beer magnate William Hamm and Charles Urschel, an oil millionaire, which the FBI investigated.

“Those were high-profile cases because at least two of the kidnap victims, their families were close friends and political contributors to FDR. So it became a big cause célèbre when they were taken and that was big money.

“The kidnappers began as bank robbers, and I think they concluded that bank robbery was risky but if you snatched a businessman off the street, you could get $100,000 or $200,000. In the Depression era, that was real money. If you had five or six bank robbers splitting $15,000, it wasn’t that much. Clyde Barrow and Bonnie Parker, they didn’t ever rob a bank that had more than a couple thousand dollars. They mostly robbed grocery stores and filling stations. They wouldn’t have been famous but for those photographs, with Bonnie smoking the cigar and pointing the gun at Clyde. It was really the romantic element that made them known. The myth.”

Therein lies another angle to Oller’s book: the romanticization of true crime. Early on, Oller introduces Charles Arthur Floyd, AKA Pretty Boy Floyd. The chapter is called “A Hood Like Robin Hood”. Stories of Floyd stealing from the rich and giving to the poor were legion. Oller recounts one, that “when Charley robbed banks, he tore up mortgages to save defaulting farmers from being foreclosed”. Oller points out that the tale is probably apocryphal, because “banks had copies”. But no matter: “To many during the Depression, banks were the enemy, and anyone who stole from them couldn’t be all bad.” Floyd was even memorialized in song, by Woody Guthrie.

Oller has told such stories on true-crime podcasts, modern-day successors to magazines like True Detective, avidly read in the 1930s. “Two or three times,” Oller says, gangsters were recognized and reported to the FBI by readers of True Detective. “Those magazines were really popular, and they’re not as inaccurate as you might think. I mean, they were pulp fiction, but sometimes they’re the best or only source, and you kind of have to make a judgment as to whether something rings true or not.”

Research and judgment calls are in Oller’s blood: he studied journalism at Ohio State then was a Wall Street lawyer before turning to writing. He happily talks of setting out to find descendants and visit scenes of stakeouts and shootouts. He has even been something of a detective himself. Among his previous books is An All-American Murder, about the then unsolved killing of a teenage girl, Christie Lynn Mullins, in Clintonville, Ohio, in 1975. In 2015, police closed the case, giving Oller “credit where credit is due”.

Oller’s other books include The Swamp Fox, about the revolutionary war figure Francis Marion, a biography of the 30s film star Jean Arthur and Rogue’s Gallery, the story of policing in turn-of-the-century New York. He’s not sure what’s next but happily talks of the Gangster Hunters, the FBI agents he wants readers to know.

“Most of these guys were law school graduates. They were not from the Ivy League, so they didn’t go to Wall Street firms. They couldn’t get legal jobs, often. So [the FBI] sounded like a good gig. So they got set up at their desks, and then all of a sudden, someone put a Tommy gun in their hands and said, ‘Go find John Dillinger.’

“Many of these guys had never fired a weapon. They didn’t know how to shoot. They certainly had never shot at another human being or had been shot at. So inevitably, they made mistakes. Over time, they adapted and became more experienced. But in the beginning, it was touch and go.”

• Gangster Hunters is out now