MCI Communications Corp. yesterday reported a profit increase of more than 400 percent for the third quarter of its fiscal year. Net income for the period ended Dec. 31 rose to $26.5 million (57 cents a share) from $5.1 million (4 cents) in the same quarter last year.

In a separate report, Virginia National Bankshares Inc. said profits declined in the final three months of 1981 but were at record levels for the full year.

Washington-based MCI made more money during the latest quarter than it made during the entire 1981 fiscal year, when it reported a profit of $21.1 million.

The bright earnings picture contrasts with the sharp drop in the price of the long-distance communications company's common stock this week. Following announcement Friday of the settlement of the government's antitrust case against American Telephone & Telegraph Co., MCI's common stock has fallen about $6 a share.

Wall Street analysts are concerned that the settlement, which will result in AT&T divesting itself of its local operating companies, might cut into MCI's competitive advantage of today in offering lower long-distance rates than AT&T.

But the third-quarter results demonstrate MCI's continued growth and appeal. Sales for the quarter rose to $140.5 million from $61.6 million.

For the first three quarters of the fiscal year, the company's profits rose to $52.6 million from $13.2 million. Sales rose by more than 100 percent to $341.6 million from $162.4 million.

Virginia National Bankshares, a Norfolk-based bank holding company, said profits from operations in 1981 rose 25 percent to $29.1 million ($4.06 a share) from $23.4 million ($3.35) the previous year. Net income, including gains or losses from selling securities, was $27.6 million ($3.84) vs. $20.4 million ($2.93).

For the final quarter of the year, operating profits declined 7 1/2 percent to $6.2 million (86 cents) from $6.7 million (95 cents). Net income was $6.2 million (86 cents) vs. $4.2 million (60 cents) in the 1980 period, when VNB listed a loss of $2.5 million from selling securities in its investment portfolio.

Chairman C. A. Cutchins III said a substantial drop in interest rates during the recent quarter resulted in a reduction of yields from loans and short-term earning assets. A slight gain in interest income was more than offset by higher operating costs.

For the year, Cutchins noted that inflation, erratic interest rates and generally sluggish loan demand "severely tested the company's ability ot operate effectively within and adverse economic environment." Assets of the Virginia firm rose to $3.2 billion from $2.7 billion, while loan volume increased to $1.8 billion from $1.5 billion.

CACI Group of Arlington, a professional research and computer firm, said earnings jumped 96 percent in the six months ended Dec. 31 to $1.7 million ($1.62) from $851,637 (83 cents) as sales soared 68 percent to more than $40 million. Profits in the second fiscal quarter rose to $972,750 (94 cents) from $415,093 (41 cents) as sales increased 72 percent to $22 million.