In the movie Wall Street, there are two monitors that look like some kind of computers with funny looking keypads. What are they? Did they really use this kind of equipment back then?
Those are actual stock trading computers used in the 1980s.
The manufacturer is Quotron - whose name is on the keypad in the second image. Quotron started providing a computer interface for reporting on and then trading in stocks back in the 1960s, and had 60% of the market in 1980s.
The "funny looking" keypads are due to the fact that they were designed specifically to support trading and the computers are not designed to be general purpose machines - for example, the number pad with fractions (share prices were set in multiples of 1/8th of a dollar), and the non-qwerty layout since the Quotron only really needed simple text input (looking up trading codes and such).
The monitors are NOT computers, but so-called "dumb terminals". The terminal will be connected to a mainframe computer somewhere in another room, probably via some kind of "front-end processor" which contains the actual logic for translating digital character and control codes in the message from the mainframe into voltages and currents used to drive the cathode ray tube (and vice versa for the keyboard input).
The black device is a special phone for traders called a turret (or dealerboard in UK/Europe). The one in the picture was made by Vband. The buttons on the left access lines or speed dials. The next section to the right is the dial pad and the last two sections are speakers.
Turrets have come a long way since then! https://www.ipc.com/iq-max-touch/