A House-Senate conference committee broke a three-month deadlock yesterday and agreed to create a new corporation with authority to spend $20 billion for development of synthetic fuels as an alternative to imported oil.

Giving a big boost to a major portion of President Carter's energy program, the conferees decided to establish a seven-member Synthetic Fuels Corp. with a 12-year lifespan.

In some cases, the corporation would have authority to make direct government investments in plants designed to produce oil from shale, and gas and oil from coal and oil from tar sands.

"We have solved the most difficult problems," said Sen. Bennett Johnson (D-La.), a key figure in negotiations with House conferees.

The conferees set a goal for the United States to produce the equivalent in synthetic fuels of 500,000 barrels of imported oil daily by 1987 and 2 million barrels daily by 1992.

After four years, the corporation would enter a second stage with a proposed ceiling of $68 billion for expanded synthetic fuels production.

Until the price of oil began shooting up, the cost of developing oil and gas from exotic sources had been prohibitive.

The new corporation is designed to find the most promising means of producing synthetic fuels, then provide the intitial financing to encourage private investment.