IF THE LATE Sen. Harry F. Byrd Sr. somehow came back to check up on Virginia politics, he'd be astounded by the goings-on. When the senior Sen. Byrd died in 1965, the Democrats held all three top state offices, both Senate seats and eight of 10 House seats. Now they occupy just the lieutenant governor's chair and four House seats, and have perennial trouble getting organized statewide. Meanwhile, the Republicans have surged ahead. Gov.-elect John N. Dalton's $1.9 million campaign was both the most expensive in Virginia history and the most sophisticated in its use of direct mail.

Virginia has clearly become a two-party state, and both parties are entering new phases - not just post-Bryd but post-Godwin and (apparently) post-Howell as well. This was summed up almost too neatly by their central committee meetings last weekend. There was the GOP, cheering Mr. Dalton and adopting a $720,000 budget for fund-raising and organizing. And there were the Democrats, trying to recoup after losing 12 of the last 16 statewide general-election contests and being told by their treasurer, "We are broke."

Both parties now have the same goal, consolidation, but their contrasting situations make the word mean different things. The Democrats are struggling to get over the rainbow and rebuild. The Republicans want to cement the broad base that Mr. Dalton and Attorney General-elect Marshall Coleman won last month.

Mr. Dalton has started by choosing Dr. Jean L. Harris, a highly regarded health administrator, as secretary of human resources, in line with his pledge to bring more blacks and women into state government.

In this competitive climate, it may seem odd that neither party wants to let the voters choose its nominee for the next big test, the contest for the Senate seat being vacted by Sen. William Scott. The Republicans' decision to hold a convention next June was almost automatic, since the GOP generally shuns primaries. The Democrats, however, usually favor primaries, but his time decided that they could not afford an expensive, divisive shootout among six or eight contenders - especially since someone might win with as little as 20 per cnet of the vote, and Republican crossover votes could have a great effect.

Under the circumstances, the Democrats' caution is understandable. A convention may indeed produce a strong candidate and let them husband more resources for the general-election campaign. The principle of primaries, however, is still sound. If both parties held them, the problems of cost and crossovers would at least be shared. State laws on campaign financing and primary run-offs may well need to be revised. Both parties should address this. After all, Virginia is one of the few states where voter turnout increased this fall - and the party that does the most to court new voters is likely to reap large benefits.