On Linux, Postgres can actually do a password-less login, using something called the Ident protocol.

Essentially, since Odoo and Postgres are running on the same machine, Postgres can ask the Operating System (the Linux kernel) the name of the system user that the Odoo process is running on, and check if the name matches the database user name. If they do, the login is automatic.

This is actually more secure than password based login, since there's no password to steal; on the other hand, it means you should run Odoo on its own Linux user, to avoid giving access to other programs.

To manually login as "postgres", you can login to the system user called "postgres" with the following command:

sudo su postgres

Then you can connect to any database on the system (try using "psql [database]").