Exxon Corp., aided by a major swing in the value of the dollar, reported first-quarter earnings yesterday of $955 million ($2.16 a share), up 37.4 percent from a year ago.

More than one-third of the $260 million increase in earnings was due to the way in which U.S. corporations operating abroad must account for paper gains and losses when currency values fluctuate.

Exxon's net on operations in the first quarter was $1.037 billion, up 19.9 percent from 1978. The net on operations, however, declined 1.1 percent from the fourth-quarter level, the company said.

Revenues in the quarter were $18.7 billion, up 23 percent from the comparable quarter last year.

The large year-over-year jump in earnings was primarily the result of tight world markets and higher prices for oil and petroleum products caused by the interruption of Iran oil production late last year. Exxon's gains exceeded the expectations of most market analysts.

Also reporting first-quarter profits yesterday was Standard Oil Co. (Indiana), which said it had a 28 percent earnings gain from the 1978 first quarter.

Most of the major oil companies will be reporting first-quarter earnings this week, and most will be affected significantly by currency fluctuations. A rule promulgated by the Financial Accounting Standards Board known as FASB 8 requires that companies report as a gain or a loss any change due to the ups and downs of the value of the dollar on their net financial obligations that must be paid in a foreign currency.

For instance, a company that borrows 100 million francs to build a plant in France must report a gain or a loss every time dollar value of that 100-million-franc debt goes up or down. However, the company is not allowed to make an offsetting assumption about what the plant itself is worth in dollars.

Because of these and other foreign exchange effects, Exxon cautioned shareholders "to use care in attempting to evaluate longer-term trends in the company's net income."

The higher Exxon operating earnings were the result of improvements abroad and in chemical operations worldwide. U.S. earnings on oil and gas operations dropped from $366 million in the first quarter of 1978 to $348 million this year.

The company said its capital investments during the quarter were $1.089 billion, about 40 percent of which was in the U.S. Of that total, $813 million was for oil and gas exploration and other types of energy projects.

News services reported the following :

Standard of Indiana reported that percent rise in earnings in the first quarter of $2.39 a share from $1.87 a year ago.

First-quarter net income rose to $349.1 million ($2.39 a share) from $273.5 million ($1.87) as revenues rose to $4.4 billion from $3.8 billion. The revenue gain was 15 percent.

Chairman E. Swearingen said the gain was primarily on overseas operations. Domestic refining, marketing and transportation earnings were lower because of higher costs.

Higher exploration costs of $544 million also reduced earnings.

American Express Co. recorded a 12.1 percent first-quarter earnings gain and spent "around $2.4 million" in connection with its unsuccessful $976 million bid for publisher McGraw-Hill Inc., Chairman James D. Robinson III said yesterday.

Robinson also said American Express' insurance division, part of the group of insurance companies covering the damaged Three Mile Island nuclear power plant in Pennsylvania, set aside "something under $3 million" in the first quarter to cover its share of possible losses resulting from the accident at the plant last month.

American Express' losses from the incident could total "just under $10 million," he said.

American Express earned $73.3 million ($1.02 a share) in the first quarter compared with $65.4 million (91 cents) in the first three months of 1978. Revenues rose from $916.9 million a year ago to $1.07 billion.

R. J. Reynolds Industries Inc. cited higher profits in its tobacco operations and benefits of the merger with Del Monte Corp. as it reported record first-quarter earnings.

RJR said earnings were $131.4 million ($2.57 a share), up 38.3 percent from $95 million ($1.94) in the same quarter of 1978.

Sales were up 24 percent to $1.97 billion from $1.58 billion for the first quarter last year.

Pan American World Airways lost $8.9 million in the first quarter, an improvement over the $24.1 million loss the carrier suffered in the first three months of last year and the best first quarter for the firm since 1968.

And Braniff International, parent company of Braniff Airlines, said it had turned a smaller profit in this year's first quarter than in the same period last year.

The Pan Am loss worked out to 12 cents a share compared with a per-share loss of 57 cents a year ago. Revenues increased 13 percent from $443.2 million a year ago to $501 million.

Like many international carriers and other airlines that don't do a lot of business on Florida routes in winter months, Pan Am's business falls off considerably in the first quarter but is high during the summer when traffic increases to Europe and other international points favored by summer travelers.

Braniff, which flies primarily through the South and thus is not affected so severely by seasonal traffice changes, said it first-quarter earnings fell to $8.1 million (40 cents a share from $8.9 million (44 cents) a year ago.

Revenues, however, rose to $283.5 million from $218.1 million a year ago.

Armco Inc. announced higher earnings of $58.38 million ($1.27 a share) on sales of $1.22 billion for the first quarter of 1979 but claimed that excessive government regulations have cost the company millions.

The earnings compared to $30.23 million (64 cents) on sales of $946.22 million for the first quarter of 1978.