The possibility exists that some online sites (and/or browsers) are now recognizing, and refusing to negotiate with, OpenSSL versions prior to 1.01g (the first bug-fix version).
Now that I've said that, I just tested my desktop OpenSSL version:
$ ssh -V
OpenSSH_6.6p1 Ubuntu-2ubuntu1, OpenSSL 1.0.1f 6 Jan 2014
And compared it to one of my own Android apps that I have updated with the latest OpenSSL version:
$ ssh -V
OpenSSH_6.6p1, OpenSSL 1.0.1g 7 Apr 2014
Both these devices work with HN and other SSL sites, but neither is running Opera.
My recommendation is that you see whether you can get an updated OpenSSL version for your phone. Use the above version numbers as a rough guide.