The House unanimously passed legislation yesterday that Rep. Thomas A. Daschle (D-S.D.), a Vietnam war veteran, said told veterans of that conflict that "for the first time we're listening" to their problems.

By a vote of 388 to 0, the House sent to the Senate a bill directing Veterans Administration hospitals to give priority medical treatment to veterans whose condition VA physicians determine is associated with exposure to Agent Orange, the herbicide used to defoliate Vietnamese jungles and which may cause various health problems.

The bill also directs the VA to expand the scope of its study of the health effects of Agent Orange to include possible effects of other toxic chemicals used in Vietnam. And the measure would extend for three years authorization for the program of storefront readjustment counseling centers for Vietnam veterans.

The Reagan administration wants to close down the centers as part of its budget cutting effort and has opposed broadening the Agent Orange study.

The House also approved and sent to the Senate by overwhelming votes bills that would extend for two years the eligibility of Vietnam veterans for on-the-job training, establish a program to provide direct or guaranteed business loans of up to $200,000 to Vietnam veterans and authorize the VA to guarantee home mortgage loans for veterans providing for graduated payments starting with low monthly amounts and increasing over the years with a person's earning capacity.

A fourth bill sent by the House to the Senate would shorten the time a prisoner of war must have been held captive to becomne eligible for certain medical benefits.