Ford Motor Co., the nation's No.2 car maker, reported a net profit of nearly $1.1 billion for the second quarter, a company record and a 54 percent improvement over that period a year ago.

Meanwhile, three of the nation's largest oil companies -- Texaco Inc., Shell Oil Co. and Phillips Petroleum Co. -- reported sharply lower second-quarter earnings, while Standard Oil Co. said it suffered a huge loss and Penzoil Corp. said its profits were down more than 50 percent from a year ago.

All five blamed the poor quarter on slumping oil prices.

This was Ford's first billion-dollar quarter since becoming a publicly held company 30 years ago. Ford said its earnings came to $4.02 a share, compared with $2.50 a year earlier. Revenue was up more than 25 percent, to $17.3 billion from $13.8 billion.

The showing contrasts with the performance of bigger General Motors Corp., which Wednesday reported net profits of $978 million, down 16 percent from 1985.

For the first half of the year, Ford's net income was $1.8 billion ($6.72 a share), compared with nearly $1.5 billion ($5.30) a year earlier. Texaco, the nation's third-largest oil company, said it netted $185 million (77 cents a share) on revenue of $7.9 billion for the quarter. In the same period of 1985, it earned $305 million ($1.28) on $11.7 billion in revenue.

For the first six months of 1986, the White Plains, N.Y., firm earned $513 million ($2.14), compared with $625 million ($2.56) in 1985. Shell, ranked seventh, said second-quarter net earnings were $219 million on revenue of $4.09 billion, compared with $317 million on revenue of $5.07 billion in the comparable period last year. The Houston company is wholly owned by the Royal Dutch-Shell Group of Cos., which is based in both London and The Hague.

Shell said it earned $495 million in the first half of the year, down from $633 million in 1985. Revenue during the period totaled $8.83 billion, versus $9.84 billion. Phillips said its second-quarter net income was $8 million (1 cent a share) compared with restated net income of $117 million (52 cents). Revenue totaled $2.34 billion, down from $3.98 billion in 1985.

For the six months ended June 30, Phillips had net income of $104 million (39 cents) on total revenue of $5.45 billion. In the same period in 1985, restated net income was $230 million (68 cents) on total revenue of $7.94 billion. Standard Oil, based in Cleveland, said it lost $681 million, after a special charge of $804 million, on revenue of $2.6 billion. That compared with second-quarter 1985 earnings of $390 million ($1.66 a share) on $3.49 billion in revenue.

For the first half of 1986, Standard Oil said it incurred a net loss of $428 million, compared with earnings of $733 million ($3.12) in the first six months of 1985. Pennzoil, based in Houston, said it netted $25.2 million (51 cents a share) in the second quarter, down 52 percent from $52.6 million ($1.12) in 1985. Second-quarter sales totaled $480 million, compared with $565 million last year.

Pennzoil said it earned $9 million (3 cents) in the first six months. That represented a 92 percent reduction from six-month earnings of $110 million ($2.32) in 1985.