By lopsided majorities, Americans say they think that President Reagan acted properly in bombing Libya and would support military attacks on Syria and Iran if those nations are found to be sponsoring terrorism, according to a Washington Post-ABC News public opinion poll.

Only one in five surveyed, however, said they think that the April 15 strike against Tripoli and other Libyan sites will reduce international terrorism or make the world safer. And four of every five people said they think that a major terrorist act in the United States is at least somewhat likely during 1986, according to the poll.

In thrust, the survey, taken from Thursday through Monday evening, shows the public strongly behind aggressive action against terrorism but wary of rocky times ahead. Three out of four people said they would be afraid to travel on some international flights or cruise ships because of the danger of hijacking or terrorism.

Among the poll's chief findings:

*Reagan's overall approval rating has jumped to 70 percent, higher than at any other time in his presidency except for a brief period after he was shot in an assassination attempt in March 1981. His rating for handling of the economy, for handling of foreign affairs in general and "for making the right decisions" in world affairs are all higher than they had ever been.

*Seventy-seven percent say the European allies are not sufficiently supporting American attempts to stop terrorism. But that feeling, based on other questions, is aimed particularly at France, not at all at England and, apparently, not at West Germany.

*The public also has shifted views on Israel and Egypt, the two major U.S. allies in the Middle East. Israel, which praised the U.S. action, is seen more favorably than at any time since it invaded Lebanon in 1982. Egypt, which criticized the attack, is seen less favorably than in any previous Post-ABC News poll.

The survey began 10 days after the raid on Libya, giving Americans time for second thoughts. Nevertheless, 76 percent in the survey said they approved of the air raid, a level slightly higher than found in polls in the immediate aftermath.

Support is extremely broad-based, with 67 percent of Democrats, 73 percent of independents and 87 percent of Republicans saying that they support the bombing. Among women, who are often highly critical of the use of force, 70 percent approved. Among blacks, where majority support is seldom found for any Reagan action, 58 percent approved.

Despite a string of terrorist incidents since the bombing, 68 percent in the survey said the strike against Libya has been more a success for the United States than a failure; only 25 percent view it as more a failure than a success.

Seventy-seven percent said the raid was justified because of the role Libyan leader Muammar Qaddafi has played in terrorist acts. However, more than half of the people interviewed said others in the Middle East aside from Qaddafi bear equal or greater blame for most terrorism.

Reagan has said the United States might attack Syria or Iran if they were found responsible for terrorist acts against Americans. In the survey 67 percent said they would support military action against those countries "if evidence is found linking" them to such acts; 30 percent said they would disapprove.

Some critics of the bombing have charged that it leaves the United States in a worsened position in the Middle East, but few Americans -- 15 percent in the poll -- say that they go along with that thinking. Instead, 47 percent think the raid leaves this nation in a stronger position in the Middle East and 37 percent see no change.

As for the European allies, the poll showed very high support for England, with 90 percent saying they consider England a reliable ally, "one that can be trusted to cooperate with the United States in almost any circumstances." American F111 bombers flew from England, with permission from Prime Minister Margaret Thatcher, to attack Libya.

Similarly, 62 percent said they consider West Germany a reliable ally, about the same as in a Post-ABC News poll in 1981.

But 54 percent in the survey of 1,505 people nationwide said they do not consider France a reliable ally, twice as many as said that in a 1981 Post-ABC News poll. France refused air rights for the planes taking off from England.

The poll suggests that the rallying around Reagan's antiterrorism moves may be having an impact on attitudes toward his policies in Central America. Forty-seven percent in the survey said they approved Reagan's handling of the situation in Nicaragua, while 40 percent said they disapproved. That is a reversal from a Post-ABC News poll a month ago, when 37 percent approved and 52 percent disapproved.

But opposition remains strong to Reagan's support for aid to the contras fighting the Sandinista government in Nicaragua. Sixty-five percent in the survey said they opposed Reagan's request to give $100 million in military and other aid to the contras; 28 percent approved giving such aid.