The "available offline" option isn't shown in Opera unless you use a user-agent extension to mask as Chrome. Once you do that, the option will show and you can enable it. It will then require you to install the "Google Docs Offline" extension just like you have to in Chrome. Once you do that, you can set files to be available offline. That works fine for me.
However, the Google Docs Offline extension isn't fully compatible with Opera and doesn't actually work offline, so you're stuck.