Norfolk Southern Corp. yesterday announced a major restructuring plan resulting in a third-quarter loss of $248.5 million, while USAir Group Inc. -- which defeated Norfolk Southern earlier this year in a battle to takeover Piedmont Aviation Inc. -- said its profit rose 76 percent in the latest quarter.

Norfolk Southern officials said the restructuring included plans to sell or abandon 2,700 miles of its 17,000-mile track system in 20 states.

Jobs are disappearing along with the track. Since 1986, the company has eliminated 1,000 positions, and it plans to cut 5,000 more by the end of 1990.

The restructuring carries a $620 million price tag, $210 million of which will be charged as the cost of track disposal and $315 million of which will be used to buy out workers' jobs. The other $95 million is being set aside to cover the cost of Norfolk Southern's casualty claim liability.

Norfolk Southern's third-quarter loss compares with its net income of $127.8 million (68 cents a share) in the year-ago period. Without the track writeoff, the company would have had a third-quarter 1987 profit of $103.3 million (55 cents).

The company reported operating revenue of $1.03 billion in the third quarter, up slightly from $1 billion a year earlier.

For the first nine months of this year, Norfolk Southern lost $1.3 million (1 cent). In the comparable 1986 period, the company earned $374.5 million ($1.98). Operating revenue dipped slightly in the nine-month period to $3.05 billion from $3.07 billion.

Norfolk Southern's 1987 nine-month results included a one-time gain of $32.8 million from the sale of 2.3 million shares of stock in Piedmont, in which USAir holds a 55.5 percent stake. USAir's application to take over Piedmont is awaiting approval by the Department of Transportation, which is expected to decide on the matter by the end of this week.

USAir said it earned $71.8 million ($1.66) in the third quarter, up from $40.8 million ($1.36) a year ago. Revenue -- which includes the addition of Pacific Southwest Airlines since last year -- rose 63 percent to $790.8 million from $486.3 million.

For the first nine months of the year, USAir earned $167.9 million ($4.82), up 153 percent from $66.3 million ($2.28) a year ago.

In other earnings reports:

Dominion Bankshares Corp. reported net income of $18.6 million (56 cents) in its third quarter, up 32 percent from $14.1 million (44 cents) reported in the same period a year ago. For the first nine months of the year, net income rose 25 percent, to $52 million ($1.30) from $41.5 million ($1.58) a year ago.

The Roanoke-based banking company, which has 265 offices, said return on average assets was 1.02 percent for the third quarter, compared with 0.89 percent the year before. Assets totaled $7.2 billion on Sept. 30, up 13 percent from $6.4 billion a year ago.

Sovran Financial Corp. of Norfolk said net income rose 16 percent in its third quarter, to $43.1 million ($1.01) from $37.3 million (88 cents) a year ago. For the first nine months of the year, Sovran's net income was $121.7 million ($2.86), an increase of 12 percent over the $108.5 million ($2.55) earned in the first nine months of 1986.

Sovran Financial operates 358 banking offices throughout the Washington area.

Harman International Industries Inc., a Washington-based consumer electronics firm, said its earnings in the first quarter ended Sept. 30 rose 49 percent to $2.5 million (30 cents) from $1.7 million (26 cents) a year ago. Revenue rose 47 percent to $98.8 million from $67.1 million a year ago.

The company, which makes high-end audio equipment, attributed the increases to stronger domestic and international sales.