I had the same issue. Office 365 wouldn't open on 64-bit Windows 7 with Avast installed. I was getting error message 0xc0000005 popping up when I tried to open Word, Excel or Outlook. After weeks of calling Microsoft all kinds of unflattering it names, I found this thread and realised it wasn't Microsoft's fault (sorry MS). Thanks to everyone for posting about it. You've saved me a ton of headaches.
I've uninstalled Avast, and Office 365 is working fine. It's a shame because I liked Avast, but the ability to do my job is more important to me than Avast is, so it's gone until they fix it.
I also had a problem upgrading to Windows 10, which may or may not be related. When I tried the free Windows 10 upgrade, it locked me out of all my files by changing the permissions on them. The only fix Microsoft gave me was reverting back to Windows 7 and wasting two weeks of my life--an unplanned/unpaid holiday from work that I wouldn't recommend--changing the permissions back. Do you think Avast caused that too? I'm wary of trying to install Windows 10 again in case it screws everything up like last time, but if anyone else had the same issue and it was Avast, I'd love to find out.