The Democratic-controlled House, urged to send a tough-fisted response to the Soviets' downing of a Korean airliner, gave final congressional approval yesterday to a compromise $187.5 billion defense authorization bill for fiscal 1984. The vote was 266 to 152.

The bill, approved by an 83-to-8 vote of the Republican-controlled Senate on Tuesday, now goes to President Reagan, who got almost all the new weaponry he wanted for next year, including the controversial MX missile as well as resumption of chemical weapons production for the first time since 1969.

Before the Soviets shot down Korean Air Lines Flight 007 two weeks ago, it was thought that the defense bill might be in trouble in the House because House-Senate conferees had included $114.6 million for nerve gas weapons that the House had voted down. But Reagan and his supporters in the House portrayed the defense bill as a way of signaling U.S. outrage over the airliner tragedy, and nerve gas critics charged yesterday that the vote was skewed by "emotionalism" over the Soviet action.

"Unfortunately, the barbarous and unjustified destruction of KAL 007 by the Soviets effectively precluded the House from considering the nerve gas issue in an objective fashion," said House Foreign Affairs Committee Chairman Clement J. Zablocki (D-Wis.), who led the fight to send the bill back to conference for deletion of the nerve gas program, the only major weapons program either house had voted to deny the president.

Rep. Ed Bethune (R-Ark.), another nerve gas opponent, said he had counted 200 likely votes against the defense compromise before the Soviets shot down the plane and accused defense contractors of capitalizing on the incident in lobbying for the bill.

Both Zablocki and Bethune said they would renew their campaign against nerve gas weapons when the defense appropriations bill, which provides the actual dollars for the Pentagon, comes up for a House vote in a few weeks.

In speech after speech yesterday, backers of the defense bill alluded to the 416-to-0 House vote on Wednesday for a resolution strongly condemning the Soviet Union, and said it would ring hollow unless Congress followed up with concrete action, starting with the defense authorization.

"The referendum today is whether we really meant what we said yesterday," said Rep. Ike Skelton (D-Mo.). Rep. Dan Daniel (D-Va.) said the Soviet leaders who ordered the plane shot down are "the same gangsters who would be making the decision whether to use gas on our troops" in any future war.

In its original consideration of the bill last summer, the House voted 256 to 161 against nerve gas production.

The Senate split 49 to 49 on the issue, with Vice President Bush breaking the tie in favor of the nerve gas outlay.

But the conferees, dominated by lawmakers who favor nerve gas production, agreed to let the program go forward.

Almost lost in the emotional crossfire was an echo, from Rep. Mike Lowry (D-Wash.), of the once loud debate over defense spending as a whole.

Lowry noted that annual spending for defense has grown by $123 billion since 1980 and asked plaintively how the country plans to pay for this large growth.

The bill authorizes $10.5 billion less than Reagan requested, but provides for $18.9 billion more than is currently being spent for defense, reflecting Congress' earlier decision to cut in half Reagan's proposed after-inflation increase of 10 percent.

It provides $4.8 billion to produce the first 21 MX missiles, $5.6 billion for 10 B1 bombers, $407.7 million for 95 Pershing II missiles for deployment in western Europe and most of the other weaponry Reagan wanted for his defense buildup.

Among Washington area members, only Rep. Michael D. Barnes (D-Md.) voted against the measure.