Mobil Corp., the nation's second largest oil company, yesterday reported its first-quarter earnings rose a modest 2.4 percent, largely because of improved profits on foreign operations.

Standard Oil Co. (Ohio), ranked 12th, attributed a 39.1 percent decline in its earnings for the opening 1983 quarter to falling crude oil prices and stiff competition in the petroleum products marketplace.

Among automakers, Volkswagenwerk AG reported a substantial loss for 1982.

Most major oil companies have announced first-quarter profit drops ranging from 15 percent to 40 percent below year-earlier results.

But Mobil, Exxon Corp. and Standard Oil Co. of California, which are partners in a consortium that produces the bulk of Saudi Arabia's crude oil, have benefitted from the kingdom's retroactive price cuts in March that reduced OPEC's benchmark crude by $5 to $29 a barrel.

In the first three months of 1983, Mobil earned $250 million (62 cents a share), up from $244 million (58 cents) in the 1982 first quarter. Revenues fell 13 percent to $14.2 billion from $16.4 billion.

Sohio's first-quarter earnings dropped to $277 million ($1.12), from $455 million ($1.85) a year earlier. Revenues fell 22.2 percent to $2.8 billion vs. $3.6 billion.

Sohio said the decision to discontinue its abrasive manufacturing operations to scale down its interests in Alaska's Prudhoe Bay field cut 1983 profits by 44 cents a share.

Sohio said its first-quarter results also were affected by a $2 million loss on refining and marketing operations as petroleum products prices fell faster than crude oil prices.

Volkswagenwerk AG said it lost 300 million deutschemarks, or about $120 million, in 1982, with the most severe losses coming in the United States and Latin America. West Germany's biggest automaker had a profit of 136 million marks--about $54.4 million--in 1981.

The company said it will propose to shareholders at the annual meeting June 30 that no dividend be paid this year.

A spokesman said the company's biggest problem in 1982 was in the United States, where sales of Volkswagens and Audis dropped 28 percent from 1981. Sales also were down in Central and South America, he said. Volkswagen invested about $600 million in its two U.S. plants. Reports have said it has since lost about $200 million of this investment.