Exxon Corp., the world's largest privately owned oil company, yesterday said the weakness of the dollar was to blame for profit decreases of 18.5 percent in the fourth quarter and 8.7 percent for the year.

The last time Exxon reported a decline in annual earnings was in 1974, when earnings dropped $2.5 billion from $3 billion in 1973, an amount inflated by the Arab oil embargo. Before then, the firm's earnings had increased steadily since 1968-69.

Other oil companies reporting results yesterday included sixth-ranked Standard Oil Co. (Indiana), with profitable fourth quarter and full year, and No. 15, Ashland Oil, Inc., which said profits dropped for the first quarter of its current fiscal year.

Exxon's fourth-quarter profits totalled $555 million ($1.24 a share), down from $681 million $1.52) a year earlier. Revenues for the three months were $15.08 billion, up 6.8 percent from $14.11 billion in 1976's final quarter.

For all of 1977, Exxon's profits totalled $2.41 billion ($5.38), down from $2.64 billion ($5.80) in 1976. Revenues were up in 10.3 percent to $58.01 billion from $52.58 billion.

Exxon said that its currency translation losses were $205 million in the fourth quarter, a period in which the dollar plunged sharply in value against leading foreign currencies. For the year, foreign currency translation losses totalled $260 million.

The company said the loss figures were the result of foreign exchange translations required under comparatively new accounting procedures.

These mandated procedures make its reported earnings susceptible to rather substantial volatility, Exxon said.

The oil giant said its profits from operations for the fourth quarter were $858 million, up 13 percent from $759 million a year ago. For the year, profits from operations totalled $3.04 billion, a gain of nearly 5 percent from 1976's $2.90 billion.

Although profits from its worldwide petroleum and natural gas operations were up 7 percent for the year, this reflected mainly higher prices, Exxon said. The volume of petroleum and gas was down.

In the United States, higher profits from its Alaskan operations - including an investment tax credit - more than offset a reduction in production of crude oil and natural gas in the contiguous 48 states, Exxon said. Profits from refining and marketing in the U.S. declined by 7.9 per cent to $267 million, mostly reflecting higher costs, the company said. Sales volume for the year was off 4.5 per cent from 1976.

Standard Oil Co. (Indiana), reported profit increases of 2.9 percent in the fourth quarter and a 13.7 percent for the year.

Indiana Standard said its fourth-quarter profits totalled $216.8 million ($1.48 a share) against $167.7 million ($1.14) in the year-ago period. Revenues were $3.8 billion, up 11.7 percent from 1976's $3.4 billion.

For all of 1977, profits totaled $1.01 billion ($6.90) against $888.2 million ($6.05) for 1976. Revenues rose by 11.8 percent to $14.2 billion from $12.7 billion in 1976.

Indiana Standard said the increase came despite a $30 million write-down of its investment in a joint copper project in Zaire. It said its profit gain reflected better results from most foreign petroleum operations, higher natural gas prices in the U.S. and Canada, and expanded domestic sales of refined oil products.

Ashland Oil, Inc., reported a 9 percent drop in profits for its first quarter ended Dec. 31 to $39.9 million ($1.32 a share) from $43.8 million ($1.56) a year ago.

The decline occurred despite a rise in revenues to $1.3 billion from $1.2 billion a year earlier. The relatively greater decline in per-share earnings resulted from a larger number of shares outstanding in the most recent quarter.

Chairman Orin R. Atkins said the drop in actual net income resulted form $10 million in added interest expense and from higher charges for depreciation, depletion and amortization.