What do Paul A. Volcker, Lee A. Iacocca and Santa Claus have in common?

They all will have an effect on interest rates in the next few months.

Three of the major factors that will determine the course of interest rates will be what action is taken by the Federal Reserve Board, headed by Volcker; how strong automobile sales will be; and how strong Christmas purchases will be, economists said.

If automobile and Christmas purchases are strong, economists said rates may rise slightly. If the Fed follows a relatively accommodative monetary policy, rates could be steady or decline in the short term. If the economy continues at its sluggish pace, rates are expected to decline for the rest of the year and through at least half of 1986, economists said.

However, at this juncture, many economists are receiving mixed signals about how strong the economy will be in the coming months and what actions the Fed will take in response. If growth is strong, the demand for credit will increase, adding pressure to rates. Strong growth also could lead to shortages and bottlenecks in production and to higher wage rates, all of which would contribute to inflationary expectations that would push rates even higher.

Additionally, some economists said that the money markets are beginning to become concerned that the Fed has allowed the money supply to grow too far above target, fueling speculation that inflation may reaccelerate next year, which would lead to higher interest rates.

Few economists, however, said they see the economy rebounding as strongly as forecast by the Reagan administration, which said growth in real gross national product will be at a 5 percent rate in the second half of the year, up from a 1.1 percent pace in the first six months. Consequently, these economists said they expected continued weakness in interest rates.

Most rates will continue their year-long decline through the middle of next year, with only a slight increase possible next month or in early November, economists said.

"Interest rates are going down the rest of this year," said Joseph G. Carson, senior economist for Merrill Lynch Capital Markets. "The pace of economic activity will slow."

After a flurry of activity caused by the recent sharp reduction in automobile financing costs by the Big Three auto makers and the stronger-than-expected employment gains in August, "the economy should go back to the underlying pace of 2 percent" real growth, Carson said.

The economy has no "fundamental new strength as the administration is claiming," said Robert Gough, senior vice president for Data Resources Inc. Gough said that private-sector debt burdens are too high for a strong surge in spending to cause the economy to rebound strongly. Without that strong pickup in activity, interest rates will rise only slightly through October and possibly early November, and then decline through the middle of next year, Gough said.

If economic activity grows at a 4 percent rate in the current quarter, interest rates will drift up slightly, Gough said.

However, "that rate of growth just can't last" because consumers' debt burdens are too high to sustain a spending boom, he said. "It depends on month-to-month economic data and Volcker."

Gough and other economists said they don't expect much change in the prime lending rate this year from its current 9.5 percent rate. Other interest rates could rise about half a percentage point through November and decline if spending is light. If spending continues to be strong, rates could be steady or rise slightly at the beginning of the year.

Other economists said they don't expect interest rates to move upward at all this year.

Some of them said it would be hard for the Fed to continue to pursue a relatively easy-money policy and push down interest rates when the money supply is growing so fast. Therefore, many economists said they expect the Fed to stand on the sidelines for the next few months, until the economy takes a decided turn one way or the other.

Nariman Behravesh of Wharton Econometrics said he expects the economy to strengthen somewhat in the fourth quarter because of the recent decline in interest rates that will promote stronger growth in the interest-sensitive housing and automobile industries. As a result, interest rates will rise very slightly and then decline.

Wharton is forecasting that three-month Treasury bill rates will decline from 7.5 percent in the second quarter to 7.2 percent in the third and then rise slightly to 7.3 percent in the fourth quarter. Those rates then will decline to 6.9 percent in the first quarter of 1986 and 6.8 percent in the second quarter as the economy weakens.

Average mortgage rates, which are hovering at about 12 percent today, will drop to about 11 percent by the end of the year and to about 10.5 percent by the begining of 1986, Behravesh said.

Merrill Lynch forecast that Treasury bill rates will drop to 6.7 percent in the fourth quarter and rise slightly to 7 percent by the second quarter of next year. Merrill Lynch also sees mortgage interest rates dropping, but rising modestly by the end of next year.