Left to right:
John O'Brien, who was present at the Columbia events of 1968 and who is an authority on progressive political buttons, reported in May 2003:
The first button with the black ink over the rest of the wording (white and red color) only showing "Strike" is a Vietnam Peace button issued by the Student Mobilization Committee (SMC) for the April 26th Strike held in 1968 around the U. S. against the Vietnam War.
The little red button was issued in Dec. 1967 for the "Stop The Draft Week" protests at the Whitehall Induction Center. It was issued by the YSA [Young Socialists Alliance] in response to the NYC Police Department having a larger red button made to identify the many hundreds of plain clothes police around that week of daily protests to "shut down the induction center". There was a later larger version made that was sold by the YSA in 1970-1973.
Here's a larger assortment of buttons from 1968-72:
Yes, that's a genuine IWW (Industrial Workers of the World, "Wobblies") button below Nixon's chin. The Panther 21 were the local counterpart of the Chicago 7 (21 Black Panthers accused of plotting to blow up Macy's, eventually acquitted); shown on the button at upper right are Panther founders Bobby Seale and Huey P. Newton ("Free Huey!"). The Panthers were a regular fixture at the Columbia gate (as were the Young Lords), selling literature and recruiting. Angela Davis was accused of complicity in the 1970 courtoom escape attempt of George Jackson (author of Soledad Brother: The Prison Letters of George Jackson) in which the judge was killed; she was acquitted too and is now on the faculty at UC Santa Cruz ("the only professor who was once on the FBI's 10 Most Wanted list"). George Jackson was killed in prison in 1971. Huey P Newton was killed in 1989. Malcom X, by the way, was killed in 1965 in the Audubon Ballroom in Harlem, now a Columbia biotech research building (Columbia restored and preserved the historic facade and built the new facility behind it).
As of July 2011, these buttons are in the Columbia University Archives in Butler Library.