Exxon Corp., the world's largest company, reported today that its second-quarter net income rose 24.1 percent from a year ago to $1.03 billion ($2.36 a share). Revenues rose 41 percent to $26.2 billion.

Nevertheless, the oil giant noted that its second-quarter profits were down 46 1/2 percent from the record $1.92 billion it earned during the first three months of this year, in large part because the value of the dollar has weakened substantailly since April.

Reported profits of major multinational companies, of which Exxon is the most important, can fluctuate widely from year to year or quarter to quarter, depending upon the performance of the dollar on foreign exchange markets. Accounting rules require companies to translate foreign earinings and revenues to current U.S dollars when reporting them to the public.

For example, Exxon siad that $314 million of its first-quarter profits were attributable to gains in the dollar, while in the second quarter the company had foreign exchange losses of $368 million.

The company's operating earnings, which exclude foreign exchange gains and losses, were $1.55 billion in the second quarter, 60.4 percent higher than in the second quarter of 1979 but still nearly 15 percent below those for the first quarter.

In a statement, Exxon Chairman Clifford C. Garvin Jr. said that the decline in operating earnings from the first quarter to the second was caused by lower sales volume of oil, gas and chemicals in the United States, narrower profit margins on those products and a decline in natural gas sales in Europe that occurs every spring.

Standard Oil of Ohio, the nation's 12th-biggest oil company, said it had second-quarter earnings of $451.3 million ($1.83 a share), 124 percent higher than the $201.4 million it earned in the second quarter of 1979.

The company reported an increase in revenues of 56 percent, from $1.82 billion in the second quarter of 1979

Sohio attributed most of its revenue and earnings increases to its improved operations on the North Slope of Alaska. The company controls more than half the production out of Prudhoe Bay oil fields.

Alaskan oil is priced much higher than curde oil produced in the contintental 48 states. Sohio said its per-barrel price of crude oil averaged $24.65 during the second quarter, compared with $15.96 a year ago.

Exxon and Sohio were the third and fourth major oil companies to report large second-quarter earnings gains. On Monday, Standard Oil of Indiana reported a 39 percent gain in profits to $488.2 million, and last week Occidental Petroleum said its earning of $191.1 million were 51.8 percent higher than the year before.

Today, Standard of Indiana boosted its second-quarter dividend from 45 cents a share to 55 cents and said it will add $220 million to its planned captial outlays in 1980.

Exxon said it will pay stockholders $1.30 a share in the second quarter, up from $1.20 in the first quarter. Last year owners of Exxon stock got 90 cents a share in both the first and second quarters.

Exxon said it earned $504 million from its U.S. oil and gas exploration and production activities in the second quarter, down from $538 million in the first quarter but well above the $348 million it earned in 1979.

It reported a sharp decline in refining and marketing profits to $29 million from $118 million in the first quarter. A year ago the oil giant earned $30 million form U.S. refining and sales operations.