Exxon Corp., the world's largest industrial company, said yesterday that its earnings fell 22 percent in the third quarter, reflecting falling world oil prices, a decline in the dollar and the expense of closing two plants in West Germany.

Exxon said its third-quarter profit declined to $995 million from $1.27 billion in the third quarter of 1984.

A stock buyback program, which reduced the number of outstanding shares, somewhat cushioned the impact of the drop in profit on earnings per share, which declined 15.8 percent to $1.33 from $1.58.

Revenue fell 5.2 percent to $22.298 billion from $23.518 billion.

Also in the oil sector, Shell Oil Co., the seventh-largest U.S. oil company, yesterday reported an 18 percent drop in earnings mainly because of lower selling prices for crude oil and chemicals and a special incentive payout to employees.

In other earnings reports yesterday, General Foods Corp. reported a 23.9 percent jump in its fiscal second-quarter profit from a year ago, on a 3.5 percent decline in sales, and Financial Corp. of America reported a modest profit in the third quarter -- only the second gain it has shown in the past 1 1/2 years as it rolled up losses of $675.4 million.

*Exxon Corp. Chairman Clifton C. Garvin Jr. said earnings were hurt by $190 million in foreign exchange losses and an after-tax charge of $135 million for closing a refinery in Hamburg and a chemical plant in Cologne as part of a move to dispose of marginal operations and improve the competitive position of the company.

For the first nine months of the year, Exxon said earnings fell 25.2 percent to $3.06 billion from $4.10 billion a year earlier.

Earnings per share dropped 18.8 percent to $4.03 from $4.96, and revenue slipped 5.8 percent to $68.531 billion from $72.731 billion.

*Shell Oil Co., based in Houston, said its third-quarter earnings slipped to $385 million from $447 million a year earlier. Shell does not report earnings per share because it now is a wholly owned subsidiary of Royal Dutch-Shell. Revenue eased to $5.42 billion from $5.28 billion.

Shell's funds from operations rose to $981 million from $900 million the year before.

*General Foods Corp., which last month agreed to be acquired by Philip Morris Inc. for $5.6 billion, said net earnings for the three months ended Sept. 28 came to $72.8 million ($1.56 a share), compared with $58.78 million ($1.20) in the same period a year ago.

Sales fell to $2.18 billion from $2.26 billion, the Rye Brook, N.Y.-based company said.

For the first six months of its fiscal year, General Foods said net earnings fell 11.7 percent to $150.5 million ($3.21), from $170.3 million ($3.37).

*FCA, whose headquarters are in the Orange County city of Irvine, Calif., is the nation's largest saving-and-loan holding company and the parent of Stockton, Calif.-based American Savings & Loan Association.

For the three months ended Sept. 30, FCA earned $12.3 million (22 cents per share), on revenue of $781 million. A year earlier it had a profit of $1.2 million -- an equivalent loss of 10 cents per share after payment of preferred dividends -- on revenue of $863.5 million.

The company's nine-month loss was $43.7 million on revenue of $2.32 billion, in contrast to a year earlier when it lost $78.4 million on revenue of $2.4 billion.

FCA also said it added $140 million to its growing delinquent loans during the third quarter, raising the total of troubled loans to $1.7 billion. The figure was $1.56 billion at the end of the second quarter and $1.13 billion at the end of last year.