It is possible in Oracle to examine the session-level settings for sessions other than your own (subject to privs obv). Is there an equivalent method in Postgres 9 or 10?
I don't think it's possible. PostreSQL session variables are meant for mostly scripts to run in the same session. If you need persisting variables across user, or a place to store state -- PostgreSQL can do that too, just use a table.
From there you can limit access to the table through Pg access permissions or getter-setter functions.
Here is an example of such a scheme, https://www.depesz.com/2009/08/20/getting-session-variables-without-touching-postgresql-conf/