HTTP Methods at the command line

I am wanting to make use of a web API from the command line.

My understanding is that HTTP Methods are as follows.

GET
POST
PUT
HEAD
PATCH
OPTIONS

When I enter these individually in Konsole it displays usage info for GET, POST, and HEAD but not for any of the others.

Why aren't all the methods available?

The GET, HEAD and POST commands on your system are likely symbolic links to /usr/bin/lwp-request, and are provided as part of LWP - The World-Wide Web library for Perl (installable on Ubuntu as the libwww-perl package):

$ dpkg -L libwww-perl | grep '/bin/'
/usr/bin/lwp-download
/usr/bin/lwp-dump
/usr/bin/lwp-mirror
/usr/bin/lwp-request
/usr/bin/GET
/usr/bin/HEAD
/usr/bin/POST

The simple answer to your question is that lwp-request does not currently implement the other methods.