How to SSH to a server behind another SSH server using JSch?
To connect to a second server behind a firewall, there are in principle two options.
The naive one would be to call ssh on the first server (from an exec channel), indicating the right server. This would need agent forwarding with JSch, and also doesn't provide the JSch API to access the second server, only the ssh command line.
The better one would be to use the connection to the first server to build up a TCP Tunnel, and use this tunnel to connect to the second server. The JSch Wiki contains a ProxySSH class (together with some example code) which allows to use a JSch session as a tunnel for a second JSch session. (Disclaimer: This class was written mainly by me, with some support from the JSch author.)
When you have your connection to the second server, use either a shell channel or a series of exec channels to execute your commands. (See Shell, Exec or Subsystem Channel in the JSch Wiki for an overview, and the Javadocs for details.)
For your unknown-host-key problem:
The secure version would be to collect all host keys (in a secure way) before and put them in the known_hosts file. (If you simply trust the key which is presented to you, you are vulnerable to a man-in-the-middle attack. If these are of no concern in your network, since it is physically secured, good for you.)
The convenient version is setting the configuration option StrictHostKeyChecking to no - this will add unknown host keys to the host keys file:
JSch.setConfig("StrictHostKeyChecking", "no");
(You can also set it individually on the sessions, if you only want to set it for the proxied sessions and not for the tunnel session. Or override it for the tunnel session with yesor ask - there the MITM danger might be greater.)
A middle way would be to enable actually asking the user (which then should compare the fingerprints to some list) - for this, implement the UserInfo interface and provide the object to the session. (The JSch Wiki contains an example implementation using Swing JOptionPanes, which you can simply use if your client program runs on a system with GUI.)
For the saving of accepted host keys to work, you must use the JSch.setKnownHosts method with a file name argument, not the one with an InputStream argument - else your accepting will have to be repeated for each restart of your client.