How to access an Oracle database from linux
Since you have root access to the server, you can su to the Oracle instance owner (typically oracle), connect to the database locally using OS authentication (e.g. sqlplus / as sysdba), and create new (or modify existing) Oracle users or roles as needed.

In case you're not familiar how su and login shells work on Linux, you will need to run su - oracle to ensure the Oracle user profile gets executed, setting up the shell environment properly. If the database was installed by an experienced person, that would include configuring all the necessary Oracle environment variables, allowing you to call its utilities, such as sqlplus.
If an attempt to run sqlplus fails with &quot;command not found&quot; or something similar, try to set the Oracle environment yourself by running, as the oracle user, source /usr/local/bin/oraenv. Note that oraenv may be elsewhere, not necessarily in /usr/local/bin, depending on your Oracle version, Linux flavour, and on how Oracle was actually installed.

Thanks to Michael Kutz  and EdStevens for valuable critique.