Exxon Corp. President Clifton C. Garvin Jr. predicted today that the Organization of Petroleum Exporting Countries meeting in Geneva on May 25 will produce little change in world oil markets currently marked by overproduction and falling prices.

"My personal belief is that not much will happen at this particular meeting," Garvin said at a press conference following Exxon's annual meeting here. Because of differing interests, the 13 members countries of OPEC "have not gotten themselves together," he said.

Several OPEC members, including Kuwait, Nigeria and Libya, want Saudi Arabia to agree to cut its crude-oil production sharply from the current level of more than 10 million barrels a day to firm up world crude markets. Saudi Arabia, on the other hand, wants OPEC to reunify its prices, which now range upward by several dollars a barrel from Saudi Arabia's of $32 for Arabian light, OPEC's benchmark crude.

"Whatever will happen will happen later" on these issues, Garvin said. Asked if OPEC were likely to pull itself back together by the time of the next semiannual meeting in December, the Exxon chairman declined to speculate.

Customer resistance to higher prices for gasoline and other products, as well as unusually high stocks of crude oil and refined products, are making refiners such as Exxon reluctant to pay the prices demanded by some OPEC countries. Meanwhile, in the United States, at least eight oil companies this week have reduced by about $2 a barrel the posted prices they are willing to pay for crude oil from domestic fields. The prices of some grades of crude have dropped from $36 to $34 a barrel, for instance.

Exxon has not reduced its posted prices, according to Randall Meyer, president of Exxon U.S.A., who declined to say whether it might do so in the near future.

Garvin said that under current conditions the entire oil industry is "having problems in the downstream end of the business."

Exxon incurred a $70 million loss on its U.S. refining and marketing operations in the first quarter of this year. Overall the corporation's first-quarter earnings of $1.6 billion were down 17 percent from their level during the same quarter in 1980.

"We are all operating in a transition period coming out of controls" on crude oil and gasoline prices, the Exxon chairman told the stockholders. "There's a lot of jockeying going on."

And because of competitive jockeying, Exxon dealers have to pay Exxon more for the gasoline they sell than the price that some independent dealers are charging the public, according to complaints voiced by dealers at the meeting.

"We are a competitive company," Garvin maintained in a reply to one dealer. But he added that there are some oil companies "with a different idea about what they want to do" in the marketplace.

Garvin and Meyer also fielded complaints from dealers about a new requirement in some parts of the country that they pay cash for their gasoline deliveries rather than use credit card slips from previous customer sales to cover part or all of the cost. Meyer said that had long been a requirement in much of the country but that the government had blocked its extension during price controls.

Meyer indicated Exxon wants to experiment with having dealers offer discounts for cash, prompting questions from reporters whether the company would like to drop credit cards altogether. Meyer ducked the question, but Garvin responded, "Yes, but not if we are the only company that doesn't offer credit cards."