well, the oratab is not that useful, I wouldn't rely on it ...

to see if an instance is running, you can :
ps -ef | grep -v grep | grep pmon
if a database ORCL (for example) is running, you will have a process called ora_pmon_ORCL

you can check, using the same command, if a listener is running, just replace pmon by tnslsnr

if you find nothing like that, you are sure that no instance is running, but is Oracle installed ???

you can look in the /etc/passwd file for a user named oracle or oracle8 or oracle73 (or whatever your sys admin wanted), if the user exists, then there is a good chance that Oracle is installed !

if you can login as root, issue a su - [oracle_user], then you can check the environment of this user to see what is declared :

env | grep -i ora

should give you ORACLE_HOME and ORACLE_SID, and your search is over

if there is no user obviously created to be owner of Oracle, then THE command for you is :

find / -name oracle -exec ls -la {} \; 2>/dev/null

which will just search for a file named oracle and will issue a ls -la of this file ...