Here's a small update for people, this information might be helpful for someone.
Unfortunately, I haven't resolved the issue yet, i tried several different installations of orchard v.1.6 and no luck, initially it was built from source codes, then - binary downloaded from codeplex, both builds throw the exception I mentioned above and
both work fine locally. I did wipe all previous files before the 1.6 installation so it's absolutely clean.
Now I'm thinking that it's something hosting-specific, I use GoDaddy economy plan and before I faced the issue above I had troubleshooted the issue with log4net:
Inheritance security rules violated while overriding member: 'log4net.Util.ReadOnlyPropertiesDictionary.GetObjectData(System.Runtime.Serialization.SerializationInfo, System.Runtime.Serialization.StreamingContext)'. Security accessibility
of the overriding method being overridden.
To fix this very first issue I used a solution provided
Now I'm rolling back to v.1.5 and will be looking the steps to replicate the issue locally, not on live website.
I'll keep you posted with the progress.