How can I connect to Oracle Database 11g server through ssh tunnel chain (double tunnel, server in company network)?

Yes, it’s possible. E.g. on Linux, run

ssh -N -Llocalport:dbserver:dbport yourname@connectionserver

where

• localport is the port on your machine which will be forwarded (can be 1521 if there is no local instance of oracle running)
• dbserver is the name or IP of the database server
• dbport is the port of the database (usually 1521)
• yourname is the login on the connectionserver
• connectionserver is the machine where you have ssh access

The same can be done on Windows using Plink (which comes with Putty):

plink -N -L localport:dbserver:dbport yourname@connectionserver

Do this on both machines (your local machine and the server you have access to) to chain the ssh tunnels. Example:

Connection server (assuming Linux):

ssh -N -L1521:dbserver:1521 dblogin@dbserver

Your PC:

plink -N -L 1521:connectionserver:1521 connlogin@connectionserver

The tnsnames.ora entry must look like you are running a local database, e.g.

prodoverssh =
  (DESCRIPTION =
    (ADDRESS_LIST =
      (ADDRESS = (PROTOCOL = TCP)(HOST = localhost)(PORT = 1521))
    )
    (CONNECT_DATA =
      (SERVICE_NAME = prod)
    )
  )