It's not an exact match, but it's possible that your father was thinking of Retrieved from the Future by John Seymour. This review of post-oil novels contains some additional information.
In Retrieved from the Future, one rural community in eastern England creates its own miniature Age of Healing in the wake of oil. It does so even as much of the rest of the nation descends into chaos and savagery around it. The novel takes place in East Anglia’s Gretford District sometime during the early decades of the twenty-first century. Its prologue is told by a fictitious publisher who informs us that this is the first book to be printed in East Anglia since the great CRASH. A collection of writings by farmers, tradesmen, soldiers, and other everyday people, the book represents an attempt to explain to future generations what happened in this rural part of England during and following the CRASH.
The novel’s story centers mostly on the Hurlocks, a local farming family that owns the totally organic, self-sufficient Cragpit Farm. Their farm is one of the most productive around, as well as one of the few that has not sold out to the huge city-based corporation London Farming. Bob and Jessie Hurlock, along with their four children, are well-prepared for the oil crisis when it finally hits. Having anticipated it for years, they have long been powering their farm entirely through wind and solar energy, as well as with methane from cattle and wood thinned from the countryside. During the initial weeks of the oil shortage, Cragpit Farm continues to thrive while London Farming struggles to keep its livestock alive and produce wheat and barley on its vast acres of oil-dependent, chemical-laden, monoculture cropland.
This newfound sense of progress is dashed when London Farming, with the backing of the British army, begins snatching up people’s farmland wholesale. Its own wheat and barley yields have failed miserably due to the loss of chemical inputs that once underpinned industrial agriculture. So the company decides to requisition the crops of all the smaller farms in Gretford District, distribute them as needed, and then give each farmer back his or her share under a ration-card system. When Bob Hurlock refuses to cooperate, he is taken prisoner and his family is sent off to a refugee camp in Sibford Maltings. Deprived of the farms that once constituted their livelihoods, the people of Gretford District now find themselves waiting in line for dole cards every Friday. As if that weren’t enough, they have to put up with the misbehavior of the British soldiers posted everywhere to keep them in line. Throughout the District, soldiers routinely go on drunken sprees of rape and pillage.
So, it's set in the United Kingdom, not the United States, and the control of gasoline only happens later, as London Farming uses the military to seize the remaining stores of oil (and, perhaps more importantly, the farmland which has been able to be tended without petroleum). Still, it hits that point of the oil being controlled by the military and farmers, although said farmers are the enemies to the more ecologically conscious Cragpit Farm residents.
Found with a search for science fiction novel agriculture controls oil. Which... in retrospect was the link that Tim posted as his "answer".