Does the US military still use these types of radio equipment?

No, they are not being used in US military service any more.
They would have been sold or given to overeas markets in a few cases.  In most cases, they would be disposed of as excess Gov't equipment.

No special license would be required other than for the frequencies used.
The GRC-106 is just HF radio, so it is just an amateur HF radio if a working one can be found:
http://www.bunkerofdoom.com/mil/106/index.html

VRC-12 and VRC-64 are just the 30-80MHz military FM (VHF) radios.
This frequency range is reserved for military use and not authorized for civilians or amateurs.  The frequencies are still used by the military, but with SINCGARS radios.

NONE of these systems include crypto.  They are compatible with EXTERNAL encryption devices.

I'm pretty sure that most military frequencies can not be operated legally regardless of what licences you have.

Catastrophes and disasters aside that is

I can't answer the first part of your question, but I'm pretty sure that you won't be able to get any of those on the surplus market due to the encryption capabilities in them (even without the crypto loaded).