E.I. du Pont de Nemours & Co.'s profits fell 23 percent in 1982 from 1981 levels and 38 percent in the fourth quarter from a year earlier under the pressure of the recession, the giant chemical and oil company said yesterday.

Among other major companies announcing results yesterday:

* Goodyear Tire & Rubber Co., the world's largest tiremaker, said earnings rose 1.7 percent to a record level last year despite lower sales and a depressed world economy.

Goodyear also said that it will acquire Celeron Corp. of Lafayette, La., an operator of natural-gas transmission systems, through a $825 million stock swap.

* Textron Inc. said a "continued weakness in the economy" depressed most of its operating divisions for a 44 percent earnings drop in 1982.

Du Pont reported a 38 percent drop in preliminary net income for the fourth quarter to $202 million (84 cents a share) from $328 million ($1.35) a year earlier. Sales were nearly unchanged at $8.4 billion.

Preliminary net income for all of 1982 was $894 million compared with pro forma combined earnings of $1.154 billion for Du Pont and Conoco in 1981. The data incorporate Conoco's results for the full year to reflect the related financial restructuring as though the Conoco acquisition had occurred Jan. 1, 1981, instead of in September 1981.

Earnings per share were $3.75 compared with 1981 pro forma earnings of $4.88. Sales in 1982 were $33.3 billion compared with combined sales of $33 billion in 1981.

"Full-year earnings for most of our traditional businesses were down sharply from 1981, primarily because of very low operating rates as a result of the recession," Du Pont's Edward G. Jefferson said. "However, biomedical products performed well despite these conditions. Both the petroleum and coal segments achieved improved performance. Earnings per share were about $1.20 higher than they would have been without the Conoco merger." Du Pont acquired Conoco for $7.8 billion.

In Goodyear Tire & Rubber Co.'s deal for Celeron, each outstanding share of Celeron common stock will be exchanged for 1.15 shares of Goodyear common stock under the terms of the merger.

Goodyear's earnings were $264.8 million compared with $260.3 million in 1981. Earnings per share were equal with the $3.59 reported in 1981. Sales for the year dipped 5.1 percent from a record $9.15 billion in 1981 to $8.69 billion.

Earnings for the fourth quarter of 1982 jumped 8.2 percent to $49.7 million (67 cents a share) from $46 million (63 cents) a year earlier. Sales fell 7.3 percent to $2.09 billion from $2.25 billion.

Textron Inc.'s 1982 net income was $84.4 million ($2.30 a share) compared with $151.8 million ($4.06) for 1981. Sales fell 12 percent to $2.9 billion from $3.3 billion in 1981.

Fourth-quarter net income was $17 million (45 cents) compared with $32 million (86 cents) a year earlier. Sales were $718 million compared with $816 million in 1981.

Textron said its machine tool divisons and operations serving the automotive and housing industries were hardest hit.

The company's aerospace and electronics divisions experienced a 22 percent drop in operating income, its outdoor products segment had a 39 percent increase in profits, and the specialty consumer unit posted a 33 percent profit decline.