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
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