The most vexing mystery in the Department of Education as summer wanes is: Who's running the general counsel's office?

At the moment, Hunter Harrison, an alumnus of the American Enterprise Institute, carries the title "acting general counsel," but government directories still list former National Review editor Dan Oliver as general counsel.

Ask Office of Civil Rights attorneys who is passing judgment on the spate of sex discrimination complaints due for decision by today, and they say, "Harrison."

Ask the receptionists in Oliver's office where he is, and they say, "not at his desk." They take messages. The calls are not returned. (A few weeks ago, if you asked where Oliver was, the answer was "on vacation." More recently, the answer was "working at home.")

Ask public affairs spokesmen in the department what's going on, and they say, "no comment." The same answer applies to questions about how there can be a general counsel and an acting general counsel at the same time.

According to friends of Education Secretary T.H. Bell, the ambiguity is deliberate. Oliver and Bell apparently had irreconcilable differences. Oliver's partisans say these involved policy, and hint that Oliver is being martyred for being faithful to President Reagan's wishes. (Bell, as an old Gerald Ford loyalist, arouses Reaganaut suspicions.)

But Bell's friends see it only as Bell--a pragmatic, Chamber-of-Commerce conservative--asserting himself as boss over a powerful intellectual who was a headstrong subordinate. Bell earned Oliver's dislike, they say, by winning the bureaucratic battle over the organization and fate of the National Institute of Education. That battle featured some of the more outspoken conservatives in the department. They, and Oliver, ended up on the losing side.

According to one associate of Bell, relations between the department's boss and his top lawyer have been prickly ever since: "They just weren't as close and didn't have the important trust relationship you need to get things done."

As for why Oliver is on vacation/working-at-home/not-at-his desk, no one is commenting, although it appears that it's just a question of time until Oliver finds another niche in the administration. ***

RIFEES' UNDERGROUND . . . The final scorecard isn't in on who goes and who stays among those affected by the mid-August reduction-in-force in the offices of Vocational and Adult Education and Elementary and Secondary Education. Department lists now show that 66 of the 456 full-time equivalent slots will be abolished and 56 people will be out on the street.

A spokesman for the management office said last week that he expected almost all of the riffed employes to find places elsewhere in the department.

That may not be necessary, if the House Government Operations subcommittee on intergovernmental relations and human resources gets its way. Subcommittee Chairman Ted S. Weiss (D-N.Y.) has asked the General Accounting Office to see if the rif and reorganization met the requirements of the 1978 law that established the department. The central issue: did Bell have to give Congress 90 days' notice before going ahead with the rif and reorganization? He didn't do that.

Whatever the results of the study, unless there is some quick court or congressional action, the rif will become accomplished fact in two weeks.

In the meantime, a few stories from the bunkers:

* The rif notices went out to the OESE in such a hurried fashion Aug. 16 that many were sloppily drawn. The result was that many of the employes being riffed were asked to walk the two blocks back to the main building so their executions could be performed again, this time with clean weapons.

* The rif and reorganization hit women hardest. In the OESE alone, 44 of the 56 employes expected to be "separated"--79 percent--were women. Unless new jobs are found for some, 64 percent of all black women in the OESE will be gone when the rif is over. Management personnel blame the civil service laws (particularly the veterans' preference feature), which the Office of Personnel Management has been trying to change.

* One of the rif victims received his notice less than 48 hours after settling a grievance filed as a result of last year's rif. The position granted him as a result of the grievance was abolished.