How to set some context variable for a user/connection

You can use a session variables in custom schema:

postgres=# set myvars.language_id = 10;
SET
postgres=# show myvars.language_id;
 myvars.language_id 
--------------------
 10
(1 row)

or via functions (http://www.postgresql.org/docs/9.4/static/functions-admin.html):

postgres=# select set_config('myvars.language_id', '20', false);
 set_config 
------------
 20
(1 row)

postgres=# select current_setting('myvars.language_id');
 current_setting 
-----------------
 20
(1 row)