Exxon Corp, yesterday reported an 18.3 percent increase in third-quarter profits to $1.36 billion ($3.13 a share). The world's largest oil company said rising crude oil and natural gas prices offset the effects of falling sales of chemicals and petroleum products.

Standard Oil Co. (Ohio) also reported higher earnings for the quarter, although -- like Exxon -- its gains over 1979 profits have begun to narrow as high prices and conservation moves forced oil inventories higher.

Exxon shares fell to $78.375 apiece, off 37.5 cents, and Sohio shares fell 25 cents to $69.50 on the New York Stock Exchange.

Exxon said its 1979 third-quarter earnings were $1.15 billion ($2.60). Sales rose to $26.75 billion from $21.68 billion a year earlier. Nine-month earnings rose 47.1 percent to $4.31 billion ($9.89) on sales of $80.62 billion from $2.93 billion $6.64) a year ago on sales of $59.15 billion. $8

Fourteenth-ranked Sohio said third-quarter profits rose 18.4 percent to $433.4 million ($1.77 a share) from $366.2 million ($1.51). Sales rose to $2.54 billion from $2.1 billion.

Sohio, 53 percent of which is controlled by The British Petroleum Co. Ltd., owns more than half the oil reserves of Alaska's North Slope and has benefited from sharply higher prices and oil output recently.

Sohio said earnings for the first nine months jumped 82.3 percent to $1.34 billion ($5.44) from $735.1 million ($3.05). The nine-month profits for this year surpassed those for all of last year. Sales climbed to $8.04 billion from $5.57 billion. The company did not report its return on shareholders' equity, a measure of profitability.

A main cause of the big rise in Exxon's net income was a $26 million gain on foreign currency translations in contrast with a loss from this source of $127 million a year earlier. Chairman G. C. Garvin Jr. said this year's operating earnings benefited from higher prices for products in the United States, Europe and the Far East and to the extent of $120 million from sales of lower-cost inventory products.

But Garvin said these benefits were largely offset by the absence in this year's quarter of a $150 million British tax benefit, by the impact of the new U.S. "windfall profits" oil tax and by lower global profit margins in chemical operations.

Garvin said domestic petroleum earnings on production and exploration were up 56 percent in the third quarter from a year ago but refining and marketing earnings dropped 2 percent. Abroad, petroleum production and exploration earnings were up 40 percent, and refining and marketing profits tumbled 34 percent.

Chemical profits fell 65 percent in the United States and 13 percent abroad.

The company's effective income tax rate fell to 62.3 percent from 68.1 percent. The return on shareholders' equity over the latest 12-month period was 243 percent, which amounts to about 14 percent after adjustment for inflation. According to Business Week magazine, U.S. oil and coal companies recorded a 25.7 percent return on equity in the year ended June 30, while all industries tallied a 15.9 percent return.

Refinery runs dropped to an average of 4.007 million barrels a day in the third quarter from 4.325 million a year earlier, and nautral gas sales fell to 7.3 million cubic feet a day from 8.4 million a year earlier.

Several other large oil companies also have said an oil-product sales slowdown -- a result of a buildup of world petroleum inventories to record levels following a 150 percent jump in foreign crude oil prices since the end of 1978 -- restrained their profit growth in the quarter.

Exxon said its worldwide petroleum-product sales volume fell 6.7 percent in the first nine months to 4.9 million 42-gallon barrels a day.

Despite the sales drop, Garvin said Exxon has increased its 1980 budget for exploration and other major projects to $8.5 billion from the $8 billion predicted in June and the $6.9 billion spent in 1979.

Speaking at an afternoon news conference, Sohio's senior vice president for finance, Paul D. Philips, cited several specific factors that have "tended to increase" the firm's earnings:

"Higher crude oil prices."

"Better margins in our marketing and refining operations."

"Higher prices for both our acrylonitrile and agricultural chemicals."

"Lower net interest costs. During the third quarter, our interest income exceeded our interest expense by $7 million."

Sohio, the 32nd-largest corporation in the United States, plans to invest $4 billion during the next five years in the Prudhoe Bay Field to keep it producing oil at a "maximum efficient rate," Phillips said.

Tosco Corp., the nation's second-largest independent gasoline refiner, yesterday reported severe earnings decline for the third quarter.

Net income was $9.3 million (44 cents a share) on revenues of $574.2 million compared with $23.6 million ($1.14) a year ago on revenues of $574.1 million.

Nine-month results were better: Net income was $55.9 million ($2.62) against $55 million ($2.61) last year. Sales were ahead slightly at $1.7 billion compared with $1.4 billion last year.

Tosco attributed its poor third-quarter performance to the federal government's entitlement regulation changes, introduced in July and retroactive to May 1. These increased the costs of Alaskan North Slope crude oil, thereby squeezing five months of entitlement costs into the two months remaining in the third quarter.