Standard Oil Co. of California (Socal) reported yesterday that its profit plunged 57 percent during the three months ended June 30, joining most other major oil companies that already have said the recession and oil glut squeezed second-quarter earnings.

Two smaller oil concerns--Sun Co. and Cities Service Co.--also said earnings dropped sharply during the period.

Socal, the fourth-largest U.S. oil company, said it earned $263 million (77 cents a share), compared with $616 million ($1.80) in the 1981 second quarter. Revenues tumbled 15 percent to $10.98 billion from $9.37 billion.

In the first half, Socal earnings fell 62 percent to $493 million ($1.44), from $1.28 billion ($3.75). Revenues fell 16 percent to $18.96 billion from $22.2 billion.

Socal said non-U.S. oil earnings were down 80 percent, and U.S. petroleum earnings declined 38 percent. Socal, based in San Francisco, blamed reduced demand, lower prices for petroleum products and the higher price of obtaining crude oil from Saudi Arabia compared with the less-expensive spot market.

In Radnor, Pa., Sun said its second-quarter profit fell 63 percent to $110 million (90 cents) from $298 million ($2.37). Revenues rose slightly to $4 billion from $3.9 billion.

In the first six months of this year, the nation's 12th-largest oil company earned $234 million ($1.91), compared with $418 million ($3.32) in the 1981 first half. Revenues inched up to $8 billion from $7.9 billion.

No. 20 Cities Service, with headquarters in Tulsa, Okla., said second-quarter earnings were off 18 percent to $74.4 million, from $90.5 million. Revenues rose to $2.127 billion from $2.121 billion.

In the first half, its profit fell 14 percent to $127.7 million from $148.2 million. Revenues increased 2 percent to $4.38 billion from $4.296 billion.

Sears, Roebuck & Co. yesterday reported its earnings were 22 percent higher than last year for the quarter ended June 30--and 26 percent higher for the first six months of 1982.

Consolidated net income for the second quarter was $163.7 million (47 cents a share), compared with $134.5 million (42 cents) in 1981. Revenues increased 8.1 percent to $7.20 billion from $6.66 billion in the second quarter last year, largely attributable to acquisitions.

For the six months ended June 30, consolidated net income was $235.1 million (67 cents) compared with $187.3 million (59 cents) last year when fewer shares were outstanding.

Revenues were $13.64 billion, up 9.1 percent from $12.50 billion for the year-ago period, also principally attributable to the acquisitions.

Results for the second quarter and first half of 1982 include Coldwell, Banker & Co. and Dean Witter Reynolds Organization Inc., which were acquired last year.

General Food Corp. yesterday reported that its first quarter earnings rose 25 percent while Nabisco Brands Inc. posted a 34 percent boost in second quarter profit from the same period a year ago.

General Foods earnings rose to $61.5 millon ($1.24 a share), from last year's depressed $49.3 million (99 cents), the company reported.

Revenue was essentially flat at $2 billion.

General Foods said the earnings increase was paced by significant advances in the company's worldwide coffee business, which had experienced depressed margins a year earlier.

It also said its domestic packaged convenience foods recorded increased earnings on higher margins.

Nabisco Brands earned $71 million ($1.11) during the second quarter of 1982, up from $52 million (83 cents) during the same period in 1981.

The 1981 second quarter report included non-tax-deductible expenses of $9.3 million (15 cents) for the July 1981 merger of Nabisco and Standard Brands, the foods company said.

The merger combined the cookies and crackers products of Nabisco with Standard Brands' products, such as Planters Peanuts and Fleischmann and Bluebonnet margarine.

Sales during the second quarter increased 8 percent to $1.5 billion, up from $1.4 billion during the comparable period of 1981.

During the first six months of 1982, Nabisco Brands earnings increased 18 percent to $130 million ($2.04), from $109 million ($1.73) during the first half of last year.

Sales for the six-month 1982 period were $2.9 billion, up 4 percent from $2.8 billion during the comparable period last year.

Bethlehem Steel Corp. announced a $47 million loss for the 1982 second quarter, compared with earnings of $77.6 million ($1.78) in the 1981 period.

Bethlehem, the second-ranked steel producer, said its sales in the latest quarter were $1.4 billion, down from $1.9 billion in the same three months of 1981.

"Bethlehem currently expects to sustain a substantial loss in the third quarter and for 1982 as a whole, although there are indications the economy may begin a gradual upturn later in the year" said Chairman Donald Trautlein.

For the six months, Bethlehem reported a loss of $113.8 million on sales of $3.35 billion compared to earnings of $103.5 million ($2.37) on sales of $3.8 billion in the same period last year.