To SSH (OpenSSH) through an HTTP proxy, you can use the
ProxyCommand config option with one of several programs that know how to talk to an HTTP proxy using the HTTP CONNECT method. The one I use is called
corkscrew and it works equally well on Linux and Cygwin.
Something like this will do the trick to let you connect through an HTTP proxy to a home server that has an sshd running on port 1234.
Host home User marc HostName dns.home.org Port 1234 ServerAliveInterval 30 ProxyCommand /usr/bin/corkscrew proxy.corporation.com 3128 %h %p
Once you have one host that you can connect to through the proxy, you can even use that host to get to other hosts.
Host webhost User marc HostName dns.webhost.com ServerAliveInterval 30 ProxyCommand /usr/bin/ssh home nc -w 600 %h %p