American college campuses may be on the verge of a nation-wide strike in response to President Nixon's speech Thursday and the American invasion of Cambodia.

Princeton, Yale, Rutgers, Ohio State, and several smaller schools are already on strike. Columbia is planning a strike beginning Monday demanding that the university put itself on record as condemning Nixon's "Operation Total Victory"

The University of Pennsylvania provost has announced that all finals will be optional because, he said, students are unable to concentrate in the wake of international developments. A mass rally is scheduled there at 11 a. m. today, to call for a strike of all East Coast schools.

After two days of disturbances and some 150 injuries, leaders of the militant strike coalition at Ohio State University urged non-violence in the continuing strike and picketing at that school. 1800 National Guardsmen remained on alert status last night, with 50 standing guard around university buildings, but the campus remained quiet.

The Ohio State strike is over black enrollment and student representation in university decisions. The strike coordinators are now also demanding amnesty for all arrested students.

'Bums'

Nixon yesterday addressed himself to the spreading protests while talking with Pentagon employees.

"You know, you see these bums, you know, blowing up the campuses," he said. "Listen, the boys on the college campuses today are the luckiest people in the world-going to the greatest universities-and here they are burning up the books.

"I mean," Nixon continued, "storming around about this issue, I mean you name it get rid of the war, there'll be another one."

The National Guard was ordered into the University of Maryland after 1500 students sacked an armory where Air Force ROTC classes are conducted.

Four thousand anti-war demonstrators at Stanford were confronted by police with tear gas after some in the crowd began trashing.

A firebomb thrown through the win-Dow of a ROTC building at Oregon State did little damage. But in Geneva, N. Y., a firebomb heavily damaged a ROTC building at Hobart College. A student was arrested and charged with arson.

Streets Blocked

University of Connecticut demonstrators were arrested after a two-hour sit-in at a downtown intersection. By-standers cheered the police as they swept through the crowd.

Five hundred students sat down in a main Schenectady, N. Y., intersection after demonstrating at Union College, a General Motors plant, and a draft board.

Temple University, in Philadelphia, has scheduled a strike for Tuesday. Yesterday police cleared away students who swarmed over an Army tank which had been involved in a minor traffic accident. There was no explanation for the tank's being moved through the streets.

Five hundred students and faculty from Binghampton University protested in front of the New York federal building.

'Absurdity'

An administration building at Marist College in Poughkeepsie, N. Y., was occupied by 100 students protesting what they termed "President Nixon's absurdity in Cambodia."

Five hundred students from Appleton, Wise-from junior high, high school, and Lawrence University (where President Pusey formerly served as president)-walked out of their classrooms and marched to a rally in front of the county courthouse.