The 1982 bull market in stocks and bonds helped Merrill Lynch & Co. post record earnings for the fourth quarter and the full year. But the effects of the recession last year and some special charges combined for a $345 million loss at Armco Inc., and three major oil companies reported mixed results.

Merrill Lynch, the nation's largest investment firm, yesterday reported fourth-quarter profits of $142.5 million ($3.48 a share), up 160 percent from $54.8 million ($1.37) in the last three months of 1981. Revenues rose to $1.6 billion from $1.1 billion.

For all of 1982, Merrill Lynch earned $309 million ($7.59), against $203 million ($5.14) in 1981. Revenues increased to $5.03 billion from $4.04 billion.

In addition to gains in commission revenues resulting from heavy trading volume in the stock market, Merrill Lynch said it had record results in the bond trading, investment management and investment banking sectors of its business.

Armco Inc., the nation's seventh-largest steel company, reported 1982 losses of $80 million from operations and $265 million in special charges, primarily in its carbon steel operations and the write-down of the value of raw materials. The loss compares with 1981 earnings of $295 million ($4.97 a share). Sales for 1982 totaled $5.4 billion, down 21 percent from $6.9 billion in 1981.

In the fourth quarter, Armco lost $53 million in operating losses and $130 million in special charges compared with 1981 fourth-quarter profits of $70 million ($1.04). Sales fell to $1.1 billion from $1.79 billion.

Standard Oil Co. (Indiana), the fifth-largest U.S. oil company, said that fourth-quarter profits rose 8 percent to $415 million ($1.42 a share) from $384 million ($1.29) a year earlier. But revenue slipped to $7.5 billion from $7.8 billion.

For the full year, earnings fell 5 percent to $1.83 billion ($6.25) from $1.92 billion ($6.56) in 1981. Revenue fell to $29.9 billion from $31.7 billion.

The company posted lower earnings from exploration and production operations for all of 1982, which were affected by reduced crude-oil prices and higher costs worldwide, Chairman John E. Swearingen said in a statement.

Atlantic Richfield Co., ranked seventh among oil companies, said fourth-quarter profits fell 7.6 percent to $434.0 million ($1.70 a share) from $469.8 million ($1.86) a year earlier. Revenue edged down to $7.095 billion from $7.14 billion.

For the full year, Arco's earnings edged up 0.3 percent to $1.676 billion ($6.61) from $1.671 billion ($6.66) in 1981. The per-share results fell because of an increase in the number of common shares, the company said. Revenue tumbled 4 percent to $27 billion from $28.2 billion.

Arco blamed higher exploration costs, lower crude-oil prices and the recession for its flat performance. In addition, its chemical, metal fabricating and metal mining operations all posted losses for 1982, mainly because of the recession, Arco said.

But Arco said its elimination of credit cards and lower gasoline prices last fall helped to increase its 1982 gasoline sales volumes by 11 percent over 1981, despite an industrywide drop in gasoline demand.

Ashland Oil Inc., which is ranked 18th among petroleum producers, said profits skidded 39 percent to $29.1 million (75 cents a share) in its fiscal first quarter ended Dec. 31 from $47.5 million ($1.40) a year earlier. Revenue slipped to $2.1 billion from $2.4 billion.

Like Arco, Ashland said much of its earnings drop reflected profit declines in several of its nonpetroleum businesses that were battered by the recession.