OWA is just a view on an MS Exchange database. It doesn't contain data itself.
So your problem seems to be: how to forward mails from your institutes MS Exchange server to your gmail account. The obvious disadvantage of forwarding, by the way: you loose the original sender and the original timestamp.
Our policy in these forums is to respect regulations from employers. So we won't help circumventing them. Just contact your IT dept and ask them how to do it. My guess is they will say: not allowed.
So I'm locking this thread.
Our (academic) institute moved from POP-based email system to Outlook Web App and have disabled all possibilities to get emails in Gmail i.e. no POP option and forwarding of emails is disabled. I absolutely love Gmail because the way it arranges the conversation and its tagging style.
The only option I see at the moment is download the emails in some email client and forward them to Gmail. I was thinking to setup Portable Thunderbird for this work but wondering if there is any other option or I should use any other email client on Win 7 home edition 64-bit.
Many thanks in advance.