Norfolk & Western Railway profits surged in the fourth quarter and were up slightly for all of 1978 despite strikes against the coal mining industry in the first quarter and an 82-day strike against N & W in the third quarter.

In the recent three months, N&W President John Fishwick said yesterday, the Roanoke-based company had operating profits of $368 million ($1.18 a share) compared with $26 million (83 cents) in the final quarter of 1977 Revenues rose 15 percent to $351 million.

For the year, N&W earned $105.9 million ($3.39 compared with $103.4 million ($3.31), as expenses and revenues both declined because of a strike against the firm by the railway clerks union. Revenues were off 12 percent to $1.1 billion and expenses declined 7 percent to $851 million.

Not included in these results from operations are one-time gains in 1978 -- tax credits resulting from an Internal Revenue Service ruling that allowed N&W a larger tax basis for its investment in the Erie Lackawanna Railway (which entered bankruptcy in 1972).

Fishwick also revealed yesterday that N&W has written down its investment in the Delaware & Hudson Railway to $500,000 at the end of 1978, reducing net income by $6.5 million (21 cents a share) before the special tax credit. N&W owns the Delaware & Hudson through a subsidiary, Dereco. The D&H also suffered a 1978 loss of $11.7 million for the year, further cutting N&W net income by 19 cents a share.

The N&W officer said Delaware & Hudson results no longer will be reflected in N&W's income statements.

Burlington Northern Inc., meanwhile, reported a slight decline in fourth-quarter profits and a 49 percent increase for the full year. The St. Paul-based rail and natural resources firm operates the nation's longest rail system, from Chicago throughout the Northwest.

Fourth-quarter profits were $20 million ($1.45 a share) compared with $20.3 million ($1.46) a year earlier. while earnings for the year soared to $114.5 million ($8.52) from $76.9 million ($5.74). Revenues (83 percent from the railroad) rose 25 percent in the recent quarter to $685 million and 20 percent in the year to $2.5 billion.