Decided to start a new thread instead of continuing to clutter http://forum.avast.com/index.php?topic=40462.15.
Today I did get some Opera hangs, but not the “opera has stopped working” message, so things seem to have improved, but not completely fixed. Config was avast! standard, network, web shield providers and OA Web Shield, Program Guard and Firewall. No changes to OA recently. Turned off OA Web Shield and the hangs immediately stopped. Nothing in OA blocked log, nothing in avast! notice and above log. So back to stable configuration with avast! standard, network, web shield providers and OA Program Guard and Firewall. Latest avast! 196 build definitely did improve Opera/OA/avast! stability for me, but didn’t entirely eliminate the problem. Maybe it’s OA’s turn next? 
Personally I would have disabled the OA web scanner in the same way I did with my firewall Outpost Pro as I also did with its email scanner. I could only see potential for conflict with two elements effectively trying to do the same task and possibly fight for control.
Though it would be nice to know why it is happening.
OA starts to have problems with avast… I’m seeing that OA is including advanced firewall protection and, maybe, some will conflict with avast. This is why we’re waiting anxious for Alwil firewall…
Yes, things work fine when I turn off the OA web shield. Interesting that it only affects Opera, not FF, but if it never gets fixed not a big thing since I can still use the avast! web shield. And, of course, figuring out why an unrelated update to avast! 196 changed how things works might help also.The email scanners are a little different. I currently need to not use Stunnel and disable them both to avoid crashing the data input/output section of the OA Firewall Status Display. But rest of the display works fine always. Turning them off is not a big issue, since all of my in and out mail goes through Gmail (my ISP outsourced to them also) so virus scanning happens anyway. Port 25 is blocked, since I now use only the Gmail ports 465 and 587 for smtp. These are all just some of the usual minor things that happen with security software. Will see what the next update(s) bring. 
Opera worked fine for a couple of days with both web scanners active, so the latest avast! 196 update definitely helped the problem. Finally got a hang that didn’t clear quickly, so did an Opera restart with no problem. Didn’t get the “Opera has stopped working” message and might have cleared if I waited a bit longer. Problem repeated briefly, so turned off the OA web shield again and problem immediately went away. Will sit like this for a while and see if it repeats without OA web shield. Problem is so seldom now it is very hard to log and diagnose, but workaround is simple. And who knows what the next updates might do after the successes of 1296.