International Telephone & Telegraph Corp. reported profit of $4.66 a share for 1978, up from $3.92 in 1977 as revenues jumped to $19.4 billion from $16.7 billion.

Net income rose to $662 million from $552 million.

Profit in the final quarter was $181 million or $1.27 a share on revenues of $5.7 billion. up from $122 million or 85 cents a share a year earlier when final revenues were $4.8 billion.

President Lyman C. Hamilton Jr. said the company expects to achieve record sales and earnings again this year. He said ITT has set a goal of earning 15 percent on stockholders' equity annually in the early 1980s.

The 1978 profit was increased $68 million by gains on foreign currency translations in contrast with a loss of $71 million on such translations in 1977.

Insurance and finance operators contributed most of the 1978 gains, and telecommunications, automotive products, foods and hotel products were quite profitable. Strikes and some other problems cut earnings of ITT's natural resources division.

ITT also announced formation of a new subsidiary, ITT Electronic Travel Services, headed by Harry Schwedock.

It will conduct a computerized multi-access travel and hotel reservation, vouchering and ticket writing system throughout the United States. It will interconnect with many other computerized reservation systems to speed up service. The company later intends to offer a computerized accounting, bill paying and checkwriting service to the travel industry.

The initial system will rent for $775 a month plus a charge of 25 cents for each ticket sold, for a package of four terminals and one printer.

The nation's largest variety chain store operator, F. W. Woolworth Co., announced record sales and profits yesterday for their fourth quarter period ended Jan. 31 and the year.

Net income for the quarter was $83.3 million, or $2.83 per share, an increase of 28 percent from last year's comparable period of $65.2 million, or $2.21 per share.

The firm attributed the strong gain to generally healthy worldwide sales performance and net favorable exchange rates. Sales and other revenue for the quarter were $2 billion, compared to the year-ago period of $1.7 billion.

The New York-based company reported yearly net income of $130.3 million, or $4.34 per share, up from the previous year's $85.5 million, or $2.81 per share.

Sales and other income for the year were $6.103 billion, up from $5.535 billion in 1977.

A company spokesman said all of Woolworth's domestic operation achieved record sales and profits in the fourth quarter. The firm operates Kinney Shoe Corp. and Richman Brothers Co., a manufacturer and retailer of men's apparel, as well as Woolworth and Woolco stores.