Atlantic Richfield Co., the seventh-largest U.S. oil company, reported yesterday that its fourth-quarter profits rose 18 percent over their year-ago level, largely because of higher refining and marketing earnings.

Union Oil Co., the 15th largest, announced that its fourth-quarter profits increased 33 percent on improved refining and marketing activities. And Ashland Oil Co., ranked 17th, had a 135 percent surge in the October-December period.

Analysts had expected the major U.S. oil companies to show a profit slump in the fourth quarter in the face of weak demand for petroleum products and lower crude oil prices.

Last week, Marathon Oil Co., the nation's 16th-largest oil firm, reported a 27 1/2 percent decline in fourth-quarter earnings that reflected costs incurred in fighting a hostile takeover bid by Mobil Corp.

In the final 1981 quarter, Atlantic Richfield earned $469.8 million ($1.86 a share), up from $398.2 million ($1.60) a year earlier. Revenues dropped 3 percent to $7.14 billion from $7.39 billion because of soft demand for chemicals and aluminum.

In 1981 Arco's profits advanced by one percent to $1.67 billion ($6.66) from $1.65 billion ($6.64) in 1980. Revenues were up 17 percent to $28.20 billion from $24.15 billion.

In the fourth quarter, Union earned $236 million ($1.36 a share), up from $177.2 million ($1.02) in the same quarter a year earlier. Revenues rose 8 percent to $2.91 billion from $2.69 billion.

For the full year, Union's profits gained 22 percent to $791.4 million ($4.56) from $647 million ($3.73) in 1980. Revenues were up 8 percent to $11.29 billion in 1981 from $10.47 billion in 1980.

Ashland, whose first fiscal quarter ended Dec. 31, posted an earnings increase to $47.5 million ($1.40) from $20.2 million (55 cents). Its first-quarter revenues climbed 19 percent to $2.34 billion from $1.96 billion.

Ashland Chairman John R. Hall said Ashland had recovered from the first quarter of fiscal 1981, when it was locked into some high-priced crude oil contracts.

"Improved refining margins and the purchase of more lower-cost domestic crude oil were the primary reasons" for the earnings' rebound in the latest quarter, Hall said. Ashland's results also were buoyed by strong contributions from U.S. Filter's Engineering & Technology operations.

American Express Co., the nation's fourth-largest diversified financial company, said yesterday that its fourth-quarter profits rose 8 percent from a year earlier, with all segments except its newly acquired brokerage unit showing good gains.

The company said it earned $132 million ($1.41) in the quarter compared with $122 million ($1.35) a year earlier. Revenue totaled $1.98 billion, a 16 percent gain from $1.71 billion in the last quarter of 1980.

For the year, American Express had net income of $518 million ($5.58) for a 12 percent gain over 1980's profit of $462 million ($5.18). Revenue increased 13 percent from $6.37 billion to $7.21 billion.

The results included operations of Shearson Loeb Rhoades Inc., Wall Street's second-largest stock brokerage, which was acquired by American Express last June 19 and rechristened Shearson-American Express.

Shearson, with a 14 percent drop in net income, was the only American Express operation not to increase earnings in the final quarter. American Express said earnings were up 29 percent in its international banking operation, 23 percent in travel-related services, and 12 percent at its Fireman's Fund Insurance Companies subsidiary.

For the year, net income rose 25 percent at Shearson, 18 percent in travel services, 16 percent in international banking and 10 percent at Fireman's Fund.

Union Carbide Corp. had lower earnings in 1981 in spite of a small sales gain, mainly because of a big shrinkage in foreign profits.

Net income for the year was $649 million ($9.56 a share), down 4 percent from $672.5 million ($10.08) in 1980. Per-share earnings were down proportionately less than net income because there were fewer shares outstanding in 1981.

Revenues rose 2 percent to $10.7 billion.

Fourth-quarter net income was $139.8 million ($2.04), down from $149 million ($2.21) a year earlier. Sales fell to $2.43 billion from $2.67 billion.

Chairman Warren Anderson said he was pleased that Carbide's domestic net income was down only 6 percent, while foreign net income was off 35 percent. He said a 4 percent increase in domestic sales offset a 14 percent drop in exports and that all international sales rose one percent to $3.19 billion.

He said the domestic sales increase occurred in spite of the divestiture of the ferroalloys division and that the best gains were made in industrial gases, Eveready batteries, Glad film products, carbon products and specialty chemicals.

American Brands Inc. said yesterday that its net income for the fourth quarter last year rose 32 percent to a record $103 million from $78 million a year earlier, while per-share earnings rose 35 percent to $1.78 from $1.32. Sales of $1.66 billion were off 8 percent from $1.80 billion the previous year.

As a result of an accounting change, the company said, net income for the period was increased by $31 million (56 cents a share) compared with a reduction of $5 million in 1980.

Net income for the year rose 2 percent to $386 million ($6.68) from $378 million ($6.50) in 1980, with sales of $6.538 billion compared with $6.801 billion.