How to configure putty for 3 hop ssh tunnel connection?

It's not clear if you are just wanting to connect to an additional machine on the same network as Linux Machines 1/2 or if you need to jump to another network beyond them (for example Machine 4 on 172.22.1.x).

If you're simply trying to get to another machine on the same 192.168.1.x network as Linux Machine 1/2, use an actual SSH Tunnel (found under Putty's Connection -> SSH -> Tunnels menu). You can set up multiple tunnels to as many machines as you need to.

If you are actually trying to get to a third network, you can open up another instance of Putty that connects via a tunnel defined on your original Putty instance.

• Define a tunnel in Putty that forwards a port on your local machine (2222 for example) to Port 22 on Linux Machine2
• Then open another Putty instance on your Windows Machine that uses the tunnel (i.e. connect to Localhost:2222) AND defines a new tunnel to forward an additional port (2223 for example) to Port 22 on Machine4 (your 3rd hop).
• Open one more instance of Putty and connect to Localhost:2223 to access Machine4

I've only ever done this with 2 hops so I don't know how it will perform. It's not an ideal solution, but it may work if this is your only option.

Edit: If you're not limited to Windows/Putty, this (Transparent Multi-hop SSH) may do what you want. If you are limited to Windows, Cygwin may have some more flexible SSH tools.