Profits of Norfolk & Western Railway decline by 56 percent in the second quarter of 1981 while earnings of the Washington Post Co. were up slightly, the companies reported yesterday.

Coal shipping, which normally accounts for more than half of N & W revenues, declined by 44 percent in the recent period because of the United Mine Workers strike. Thus, earnings were off sharply to $26.2 million (80 cents a share) from $59 million ($1.88) as revenues dipped 14 percent to $351 million.

Because of an unusually strong January-March quarter, however, the Roanoke-based railroad's earnings for the first six months of 1981 were down just 2 percent from last year to $104.8 million ($3.23) from the record $107.4 million ($3.43) in the same 1980 months. Revenues rose 3 percent for the six months to $800 million.

"With the coal strike settled, we look fro strong coal traffice the remainder of this year," said N & W Chairman John Fishwick. He noted that shipments of motor vehicles and parts were up by 20 percent and 14 percent, respectively, in the quarter -- the first such gains since 1978.

The Interstate Commerce Commission is considering a proposed merger of N & W with Washington-based Southern Railway.

Washington Post Co. profits in the second quarter were $13 million (92 cents a share) compared with $12.6 million (90 cents) a year earlier as revenues rose by 14 percent to $194 million. A company statement said all three divisions -- newspapers, broadcasting and magazines -- had higher revenues and pretax profits in the quarter.

In addition, the communications firm said its share of earnings from affiliated businesses was $1.1 million in the recent three months compared with $400,000 a year earlier, an increase that reflects operating improvements at a Virginia newsprint factory in which the Post Co. is a major partner.

Reflecting lower earnings in the year's opening quarter, Post Co. profits in the first half were down to $14.8 million ($1.05) from $164 million ($1.17) although revenues rose 12 percent to $360 million.

Acacia Mutual Life Insurance Co. of Washington said life insurance sales in the first half of 1981 rose 11.6 percent to more than $368 million, with net investment income up by the same percentage to $29.4 million.

Total life policies in force rose $122.6 million to more than $4.8 billion, while assets on June 30 stood at a record $844 million compared with $825 million at the start of the year.