First Virginia Banks posted a record net of $18.4 million ($1.47 a share) for the first nine months of 1982, up more than 25 percent from the $14.6 million ($1.17) earned in the first three quarters of 1981.

Last year's earnings were restated to reflect the acquisition of two banks earlier this year, which helped push the Falls Church bank holding company's assets to $1.9 billion, an 11 percent increase over 1981.

First Virginia Banks' third-quarter net jumped 34 percent to $6.5 million (52 cents) from $4.8 million (39 cents). Higher interest rates and the increase in assets provided the boost in profits, said Chairman Thomas K. Malone Jr.

Madison National Bank's earnings for the first nine months of 1982 climbed 18 percent to $2.25 million ($5.50) from $1.91 million in the same period a year ago. Third-quarter net increased to $721,000 ($1.76) from $584,000 ($1.42), and the bank's assets were up 9 percent to $201 million.

Annual earnings were off by about one-third at Williams Industries Inc. of Merrifield, and Tech Serve Inc. of Beltsville posted a loss for its latest fiscal year.

Williams, a crane and construction-equipment company, said earnings dropped to $400,000 (41 cents per a share) from $580,000 (62 cents), while revenues slipped to $8.1 million from $8.7 million. Despite the off year, Williams Industries declared a 10 percent stock dividend to be paid Nov. 30 to shareholders as of record Oct. 25.

Tech Serv, which makes radio-controlled target planes for the military and other electro-mechanical products, showed a loss of $27,500 on sales of $3.1 million for the year ended June 30, down from earnings of $19,000 (3 cents) on sales of $2.6 million the previous year.