Ignoring administration objections, the House last night adopted an expensive new four-year farm bill after inserting provisions under which food stamp fraud investigators could in the future carry firearms and make arrests.

Final passage came on a 192-to-160 vote after another day of fractious debate that set the House in sharp opposition to the White House.

The divisions that characterized most of the debate, pitting economizers and critics of special interests against a once-formidable and unified farm coalition, showed up again just before final passage.

A Republican effort to limit the terms of the measure to two years instead of the customary four was rejected by a slim margin of 13 votes after tempers flared and voices soared in a debate over how farm interests were best served.

It was, in a way unknown to previous Congresses, a farm bill that pleased no one--farmers, the administration, consumer groups nor legislators from major agricultural areas--because of budget restraints imposed by the White House.

After final passage, Rep. Kika de la Garza (D-Tex.), chairman of the Agriculture Committee, reflected on the general discontent, saying the bill was a compromise that maintained "most basic safety net programs" for farmers, yet stayed within fiscal 1982 budget limitations.

Administration strategists, frankly disappointed with the outcome in the House, indicated they will aim at the upcoming House-Senate conference to reduce costs of the legislation.

According to the Department of Agriculture, the House bill will cost $16.2 billion over the life of the measure. The Senate version--acceptable to the White House--carries an estimated cost of $10.6 billion.

But it wasn't just money that separated the administration and the House, where legislators refused to bow to demands for lower price support loan levels and target prices for wheat, feed grains and rice.

They were at odds, for example, on a bitterly debated amendment by Rep. Glenn English (D-Okla.), adopted by a 223-to-162 vote, barring the import of meat produced with drugs or chemicals not allowed in U.S. meat production.

The English amendment, supported strongly by the National Cattlemen's Association, was advertised as a pro-consumer step, but the administration contended it would set off retaliation by U.S. customers overseas.

And the administration apparently was less than unified on the question of giving USDA's inspector-general's agents police powers. USDA wanted the new powers, but the White House and Department of Justice reportedly opposed the amendment as proposed by Rep. E. Thomas Coleman (R-Mo.).

As written originally, Coleman's amendment would have allowed inspector-general investigators to carry firearms, make arrests and searches and seizures without warrants in cases where they believed criminal violations of food stamp law were occurring.

Critics such as Reps. Peter W. Rodino Jr. (D-N.J.) and Thomas N. Kindness (R-Ohio) charged that the sweeping language would seriously violate constitutional rights and was a dangerous expansion of police powers.

A redrafted version, worked out on the floor, removed the power of seizures and searches without warrants, but retained authority for USDA's T-Bone Cops to make arrests when they witnessed cases of felony fraud involving food stamps.

Rodino, chairman of the Judiciary Committee, said the amended version still caused him concern. Creation of the new national police agency, he said, "could be another grave hole in the Bill of Rights . . . we have fought revolutions over search and seizure issues."

"We have to deal with food stamp abuses, but we have agencies that can be called upon to do that. The Department of Justice is the central law enforcement agency, and maybe one day we'll recognize that this enforcement power ought to be there," Rodino said.

But Coleman argued that the 260 agents in the USDA inspector-general force are hampered seriously in battling food stamp fraud because they cannot deal swiftly with criminal violators and must depend on unreliable assistance from other law enforcement groups.

"We're talking about police-type investigations that the inspector-general people conduct and we are lucky that none of them has been killed or wounded so far," Coleman said. "My concern is to provide protection for the agents and an idea, too, is to spur more action by other enforcement agencies."

The new enforcement powers for USDA were part of a portion of the bill setting a fiscal 1982 spending limit on food stamps at $11.3 billion and formalizing eligibility rules that will reduce participation by about one million during the next 12 months.

The food stamp section met with administration approval, but other portions of the bill made it a front-running candidate for presidential veto.

The House, for example, refused to follow the Senate-White House line and reduce target prices and support loan rates for major commodities. The House version also contains dairy-support provisions the White House says are too costly,