The nuclear-arms protest movement came home to America again yesterday, steering clear of the streets and settling peacefully onto more than 150 college campuses across the country in a Veterans Day "teach-in" about nuclear war and the escalating arms race.

The nationwide teach-in differed markedly from the movement that re-emerged in Europe last month, where hundreds of thousands marched to protest plans to deploy new nuclear weapons in the North Atlantic Treaty Organization. Those demonstrations, in several countries, were reminiscent of the ban-the-bomb anxiety of the 1950s and 1960s.

But sponsors of the American teach-ins, the Union of Concerned Scientists based in Cambridge, Mass., contended the Veterans Day rallies and speeches represented the largest American antiwar demonstration since the Vietnam protests.

Across the country, the campus speakers ranged from Hans Bethe, a physicist who worked on the Manhattan Project, to Paul Warnke, who was President Carter's chief SALT negotiator, to retired general James Gavin, former ambassador to France and a Vietnam-war critic.

In Boston, Warnke told a Harvard audience that the escalation in nuclear arms added nothing to the security of either the United States or the Soviet Union. "Militarily, these new weapons add nothing to our strength," Warnke said, "but our leaders see them necessary as sending the 'correct message.' "

Warnke said public involvement in the issue of arms control is "essential" but has been "sadly lacking over the past decade" in the United States.

The Boston audience also heard from Yuri Kapralov, consul from the Soviet Embassy in Washington, who said the American arms buildup, including the MX missile and the B1 bomber, "for us resembles very much the preparation for nuclear war."

At the Georgetown University Law Center here, a crowd of about 350 heard Rep. Morris K. Udall (D-Ariz.) compare the quiet Veterans Day "teach-in" to the beginning of the Vietnam protests, in which "the people got ahead of the politicians" and brought about major policy changes.

Udall criticized the increasing discussions of limited and theater nuclear wars as "this insane idea that the Soviets will take out Omaha at 9 a.m., lob some at a few air bases at 10 a.m. and then we'll all go to lunch at the Madison Hotel and decide what to do next."

The nationwide activity was confined mostly to academic settings on college campuses, with little overflow into the streets--a strategy which the demonstration's organizers said was the way they wanted it.

"I'm not a take-it-to-the-streets type myself," Dr. Henry W. Kendall, a physics professor at Massachusetts Institute of Technology and chairman of the sponsoring Union of Concerned Scientists, told reporters. "When things get that far along, they're out of joint."

Kendall said he opposed unilateral disarmament and policy changes by "spasms and splurges." Disengaging from the nuclear arms race should be done with "exquisite care," he said, because it is "more complicated backing down than going ahead with a mindless buildup."

Still, Kendall warned that the new escalation of nuclear arms presented the superpowers with a "last chance to negotiate a halt to the arms race before the whole frightening process gets completely out of hand."He said new weapons systems, which could be deployed in a few years, included "miniaturized missiles up to Stars Wars technology that will surround the planet with orbiting nuclear forces."

The long-planned Veterans Day teach-in by the scientists also spurred other protest activities.

In Groton, Conn., about 150 demonstrators protested peacefully near the shipyard at which Vice President Bush and Adm. H. G. Rickover participated in the commissioning of the nation's first Trident nuclear submarine, the USS Ohio. Five demonstrators were arrested when they tried to block buses carrying dignitaries to the base.

In California, protesters launched a drive for 500,000 signatures to place a symbolic initiative on the state's 1982 ballot calling for a mutual freeze on new nuclear weapons by both the United States and the Soviet.