Norfolk & Western Railway Co. and Burlington Northern Inc., two of the nation's largest rail firms, yesterday reported strong gains in profitability and business volume during 1979. Seaboard Coastline Industries, which operates one of the two major Southeast rail networks, also reported higher earnings.

Energy needs, particularly a boom in coal shipments, contributed to the banner years for N&W and Burlington. N&W, based in Roanoke, earned $199 million ($6.36 a share) in 1979, up 88 percent from operating earnings of $106 million ($3.39) before an extraordinary credit of $59 million.

Revenues rose 32 percent to $1.45 billion last year.

Fourth-quarter earnings rose to $57 million ($1.83 a share) from $36.8 million ($1.18).

Burlington Northern, based in St. Paul, reported 1979 earnings of $176 million ($13.11 a share), up 53 percent from $114.5 million ($8.52) the previous year. Revenues of the transportation and natural resources firm rose 28 percent to $3.3 billion.

Fourth-quarter profits rose to $50 million ($3.68) from $20 million ($1.45), with revenues up 33 percent to $908 million.

Seaboard Coastline, based in Jacksonville, said earnings for 1979 were a record $132.6 million ($9.06 a share) compared with $67.7 million ($4.64) a year earlier, when profitability was trimmed sharply by one-time charges. Transportation revenues rose 16 percent to $2.1 billion for the company, which operates the Seaboard Coastline and Louisville & Nashville railroads. w