U.S. Steel Corp., the nation's largest steel producer, yesterday reported net income surged 50 percent to $167.6 million ($1.89 per share) in the second quarter of 1981 from $111.5 million ($1.28) in the same period a year ago.

Chairman David M. Roderick noted the earnings gain was achieved despite an after-tax cost of over $50 million resulting from the strike against the soft-coal industry. Roderick said the 1980 second-quarter earnings included a $30.8 million extraordinary tax credit. Before the credit, net income came to $80.7 million (93 cents).

Sales for the quarter rose to $3.8 billion from $3.15 billion a year earlier.

Income for the first half of 1980 amounted to $438.5 million ($4.95) on sales of $7.2 billion, compared with $237.5 millon ($2.73) on sales of $6.3 billion for the same period a year ago.

Textron Inc. reported it earned $1.15 a share on continuing operatins, up from $1.12 a year ago. First-half operating profit rose to $2.24 a share from $2.20 a year ago. The report includes discontinued operatins or those being phased out by Textron.

Net income for the quarter was $43.4 million ($1.16 a share) on sales of $869.5 million, compared with $41.7 million ($1.12) a year earlier on sales of $850.6 million.

First-half net was $84.5 million ($2.26) on sales of $1.72 billion, compared with $79.7 millon ($2.13) a year ago on sales of $1.65 billion.

Amax Inc., the metals and minerals combine, yesterday reported sharply lower earings of $1.41 a share for the second quarter of 1981 against $2.22 a year earlier.

Net income was $95.09 million on sales of $699.96 million, down from $141.21 million a year ago on sales of $689.13 million.

First-half profit was $165.17 million ($2.45 a share) on sales of $1.461 billion versus $281.47 million ($4.66) a year ago on sales of $1,561 billion.

Chairman Pierre Gousseland said worldwide depression in the metals business, which might end late this year, caused Amax's problems.

American Broadcasting Cos. Inc. reported profits rose 3.4 percent in the second quarter to $55.6 million, becoming the only parent of a broadcasting network to report a gain for the April-June period.

Network television profits rose even before a bookkeeping change that added $2.6 million (9 cents a share) to second-quarter earnings.

Earnings for the second quarter came to $1.96 a share on record revenues of $612.3 million, compared with earnings of $53.8 million ($1.91) on revenues of $578.5 million in the same 1980 period.

In the first six months of the year, earnings fell 12.4 percent of $68.4 million ($2.41), compared with profits of $78.1 million ($2.77) in the first six months of last year. But revenues rose 2 percent to a record $1.15 billion from $1.13 billion a year earlier.

Times Mirror Co., owner of The Los Angeles Times and The Denver Post newspapers, said yesterday its second-quarter earnings were $38.5 million ($1.13 a share) on revenues of $539.5 million.

In the same quarter last year, the company earned $35.8 million ($1.05) on revenues of $517.8 million.

However, Times Mirror said it had changed accounting periods during 1981, with this year's second quarter being 21 days shorter than last year, and the six-month period being 16 days shorter.