The House voted overwhelmingly yesterday for a bill designed to reorganize the troubled Farm Credit System and offer last-resort federal financial support to the country's largest agricultural lender.

The bill swept to passage, 393 to 32, after sponsors made last-minute changes sought by the Reagan administration. These require that any bailout money for the FCS must go through the regular congressional appropriations process.

The bill now goes to a conference committee to resolve differences between the House and Senate versions. The chief difference involves composition of a capital corporation board that would oversee reallocation of FCS assets.

House Agriculture Committee Chairman E (Kika) de la Garza (D-Tex.) conceded that the bill would not provide the direct aid sought by the FCS but said it would send an "important message" of congressional support to the bond market.

Like the nearly identical Senate measure, the bill requires major FCS internal-management changes and use of the system's reserves before it can obtain access to federal funds to prop up its embattled loan portfolio.

A major feature of both bills is creation of a capital corporation within the FCS to control transfer of funds from healthy banks to ailing sections of the system and to take over properties on which borrowers can no longer pay.

The bill also would give the federal Farm Credit Administration new regulatory powers to oversee the FCS, which holds about one-third of the nation's $214 billion agricultural debt.

Meanwhile, House and Senate conferees spent much of yesterday on inconclusive efforts to break rock-hard deadlocks over spending portions of a final farm bill.

The conferees abandoned attempts to settle less controversial "miscellaneous" differences so some members could attend the annual White House Christmas party for members of Congress.

Conference leaders earlier met with President Reagan and heard a new warning that he would reject a bill that does not meet spending requirements -- $50 billion over three years and a one-year freeze on income subsidies.

"The president said he wanted a bill he could sign, but I told the president he couldn't have it both ways," de la Garza said. "A bill with his philosophy would cost more than a bill we could send him that meets the budget."

Both the House and Senate versions are at least $6 billion over the administration's limit, and both exceed the White House demand for a one-year freeze on direct subsidies to farmers.

The Senate bill calls for a two-year freeze on the subsidies, known as deficiency payments, while the House would freeze them at current levels for five years. Both sides appeared deeply dug in yesterday, unwilling to compromise.

Rep. Edward R. Madigan (Ill.), ranking GOP member of the House committee, said his fellow House conferees were "in unanimity" on insisting that the bill contain at least a four-year freeze on income subsidies. Freeze proponents say the subsidies are vital to farmers to offset lower market prices that both bills mandate for wheat, corn, rice and cotton.

Another sticking point is dairy provisions. House conferees from both parties made it clear that they would not readily give up their "diversion" plan to pay farmers to cut milk production, a plan Reagan has warned that he would veto.

The Senate would drop milk price-support levels in 1987 and subsequent years as a surplus-cutting device. The administration is insisting that the cuts begin next Jan. 1 to avoid more federal spending and acquisition of surplus milk, butter and cheese.