The Senate yesterday sent President Reagan the final version of legislation aimed at curbing Soviet espionage at U.S. embassies and barring the Palestine Liberation Organization from setting up new offices in this country.

The bill grants more than $8 billion in spending authority to the State Department and other agencies over the next two years. The bill also authorizes full payment of U.S. contributions to the United Nations and other international groups.

Recently, the State Department has taken many cost-cutting steps in an effort to meet deficit-reduction goals, but the bill reverses some of them.

For example, it keeps open several U.S. missions threatened with closings, including consulates at Strasbourg, France; Goteborg, Sweden; Dusseldorf, West Germany; and Edinburgh.

The measure also includes a range of new requirements . Among them are:

Improving security at U.S. missions abroad, including phasing out the use of citizens of communist nations in areas where classified material is stored. The move underscores concerns in Congress that employing foreign nationals in such countries as the Soviet Union unnecessarily exposes the U.S. diplomatic missions to espionage.

Requiring Reagan to certify that he will act to eliminate any intelligence threat from the new Soviet Embassy at Mount Alto in northwest Washington, one of the highest points in the capital. The bill also requires the president to certify that the new U.S. Embassy in Moscow, riddled with listening devices, will be secure upon completion.

Barring the Palestine Liberation Organization from establishing new offices in the United States. Foreign Relations Committee Chairman Claiborne Pell (D-R.I.) said that the PLO observer mission to the United Nations would not necessarily have to be closed in light of legal interpretations of U.S. obligations under international law.

Prohibiting the State Department from soliciting or accepting money to acquire a residence for future secretaries of state.