The Senate yesterday approved, 78 to 12, and sent to the House for final congressional action a major energy bill setting up a $20 billion program to encourage domestic production of synthetic fuels as alternatives to foreign oil.

A companion bill to cut government red tape and get new energy production programs off to fast starts also has cleared a House-Senate conference and is expected to receive final congressional approval soon.

The synthetic fuels bill would encourage production through a variety of procedures, ranging from loan and price guarantees to government production if necessary to speed the search for economically feasible new energy sources such as turning coal to gas and extracting oil from shale.

The goal is to produce the equivalent of 500,000 barrels of oil a day with this first installment of $20 billion by 1987. The next step could be to put up $68 billion more in federal money to raise synfuel production to two million barrels a day by 1992. That is more than 10 percent of present comsumption in this country.

The bill also authorizes $5 billion during the next five years for other energy programs. It authorizes $1.45 billion to find ways to create energy from farm, forest and urban waste. It would set up a solar bank to subsidize loans to install solar energy systems and would make grants to help the poor insulate homes.

As their final action this week the synfuels conferees agreed on language directing the president to resume building up the billion-barrel strategic oil reserve that Congress provided for in the 1978 omnibus Energy Act. So far, only 90 million barrels have been put into underground storgage for use in an emergency. The administration stopped adding to the reserve last year as part of an agreement by which Saudi Arabia agreed to increase oil production to make up for the Iranian cutoff.