So, you want the traffic from the oracle box to be forwarded through the linux box (over ssh) to your work computer? If that is the case, that's pretty easy. And, assuming your SSH server on the linux box is set up to allow it, you can specify ports to forward on the client side.
I did the same thing several months ago: I needed to access a window$ box within my network remotely (Windows Remote Desktop/Terminal Services). So, I just opened up port 22 to my linux box to establish an ssh session. Then, I just set up putty (my preferred client) to specify traffic to localhost:5518 on the client to go to 192.168.0.2:5518 (the windows box on the remote network) over ssh.