Two Northern Virginia banking companies-one of the oldest and one of the youngest-announced yesterday that they have started talks about a possible merger. Separately, two Virginia savings and loan companies also revealed plans for a proposed combination.

New Virginia Bancorp. of Springfield and National Bank of Fairfax said their boards of directors each voted to proceed jointly on negotiations that could create a banking company with about $350 million of assets.

The proposed S&L combination involves Virginia First S&L of Petersburg, a $208 million institution that offered to buy all shares of United Savings and Loan in Arlington, which has six offices and deposits of about $66 million.

For both Virginia First and United S&L, the new proposed combination is the second time around on the Northern Virginia merger trail. Heritage Financial Corp. of Richmond tried to buy United last year, but the Arlington firm's directors ultimately rejected the bid as inadequate. And Virginia First tried earlier this year to acquire Family S&L.

The announcement by National Bank of Fairfax and New Virginia Bancorp. yesterday provided few details about their merger talks.

Changes in Virginia banking laws in recent years have intensified a trend toward consolidation of financial institutions into statewide organizations, with increased capital bases and the ability to engage in larger loan transactions.

Founded in 1902, National Bank of Fairfax has a dozen offices and assets exceeding $170 million. Deposits at the end of 1978 totaled about $147 million.

Profits of the Fairfax bank last year were a record $1.8 million ($5.33 a share), and compound annual growth of earnings per share since 1974 has been 23 percent compared with a 17 percent average for all Virginia bank firms, according to a recent survey by Johnston, Lemon & Co., the Washington investment firm.

New Virginia was organized as a bank holding company in 1975 for Northern Virginia Bank, with a goal of expansion through acquistions and new businesses. Stockholders of the Bank of Warrenton rejected a New Virginia takeover bid in 1977, but the Springfield firm was successful last year in acquiring First City Bank of Newport News.

With 10 offices in Northern Virginia and four in the Newport News area, New Virginia had assets of $180 million at the end of 1978 and deposits of more than $159 million. New Virginia earned $1.7 million ($1.31 a share) in 1978 and has a compound annual growth in earnings per share of about 31 percent-the third highest of major regional banking companies.

In the separate Virginia First-United S&L talks, the Petersburg company plans a cash tender offer to United holders at $16.85 a share. United said its board "unanimously approved the proposed offer."

The companies said the tender offer is conditional on the preparation of a definitive agreement, Virginia First acquiring not less than 51 percent of United shares and regulatory agency approval.

Virginia First operates 10 offices in the Richmond-Petersburg area, and its officers are said to be anxious to penetrate the Washington area market.

Last fall, Heritage had offered 1.5 shares of its common (a value of about $20) for each share of United. Financial Mortgage and Realty Corp. owns 25 percent of United shares, having purchased most of them in 1978 for $12 a share. In recent days, United stock has been quoted at under $10 a share.