I'm very new to SSH, and what all you can do with it and I recently began to wonder how I would go about SSHing into a computer that's SSHing my server, through my server. I know I can SSH a computer on the network I'm on, but I've had trouble doing the same thing long distance via my server. I'm sorry if I'm not coming across very clearly, if you need me to elaborate in anyway don't be afraid to ask and I'm open to any and all suggestions.
With SSH there is a server and a client. Quite literally your Web Server(or what ever machine that has it installed already) has an SSH Server software installed on it that allows you to use your SSH Client software to login. If you want to login to the SSH user that is using the client to login you can do that, but you will need to install an SSH Server on that machine.
Here is a guide https://help.ubuntu.com/14.04/serverguide/openssh-server.html
It is pretty simple to start as long as you don't have a firewall/router that is blocking your the SSH User.
To sum up the guide though and if you aren't blocked further up the network it is as easy as installing the ssh server.
use this command on the original user machine
use this command on the original server machine
Then just login from what ever machine you want using that details you posted above.
Let me know if this helps.