Login into Oracle Database Error
There could be various reason for this error.
 You are using wrong ORACLE_SID and ORACLE_HOME.
 The instance that you are trying to connect isn't up and running.

When you have wrong ORACLE SID and HOME.

I could reproduce the error by changing my SID to something else. My SID is oracdb.

[oracle@myserver ~]$ ps -ef | grep pmon
oracle   29336     1  0 Apr27 ?        00:00:22 ora_pmon_oracdb


But I changed it to orcl.

[oracle@myserver Desktop]$ export ORACLE_SID=orcl


Then I tried to connect to the database using SQL*PLUS.

[oracle@myserver Desktop]$ sqlplus sys

SQL*Plus: Release 12.2.0.1.0 Production on Tue May 2 00:23:50 2017

Copyright (c) 1982, 2016, Oracle.  All rights reserved.

Enter password: 
ERROR:
ORA-01034: ORACLE not available
ORA-27101: shared memory realm does not exist
Linux-x86_64 Error: 2: No such file or directory
Additional information: 3701
Additional information: -923528497
Process ID: 0
Session ID: 0 Serial number: 0


Then I changed it to original SID.

[oracle@myserver ~]$ export ORACLE_SID=oracdb
[oracle@myserver ~]$ sqlplus / as sysdba

SQL*Plus: Release 12.2.0.1.0 Production on Tue May 2 00:28:40 2017

Copyright (c) 1982, 2016, Oracle.  All rights reserved.


Connected to:
Oracle Database 12c Enterprise Edition Release 12.2.0.1.0 - 64bit Production


When your instance is down and connected as a non-sys user

Use the following linux command to check whether some of the important background processes are running or not such PMON or SMON.

[oracle@myserver ~]$ ps -ef| grep pmon
oracle   57587 57044  2 00:52 pts/3    00:00:00 grep pmon


My oracle instance is down.

Now, as you have tried, I attempt to connect to the database using non-sys user, sysdba is a privilege not a database user.

[oracle@myserver ~]$ sqlplus sysdba

SQL*Plus: Release 12.2.0.1.0 Production on Tue May 2 00:53:04 2017

Copyright (c) 1982, 2016, Oracle.  All rights reserved.

Enter password: 
ERROR:
ORA-01034: ORACLE not available
ORA-27101: shared memory realm does not exist
Linux-x86_64 Error: 2: No such file or directory
Additional information: 3701
Additional information: -688980181
Process ID: 0
Session ID: 0 Serial number: 0


Enter user-name: 


I got the same error as you have got.

Now, connect as sysdba/sysoper and start the database instance.

[oracle@myserver ~]$ sqlplus / as sysdba

SQL*Plus: Release 12.2.0.1.0 Production on Tue May 2 00:53:36 2017

Copyright (c) 1982, 2016, Oracle.  All rights reserved.

Connected to an idle instance.

SQL&gt; startup