ok, that was my very stupid mistake. I post the answer here just in case someone has the same problem.
The correct path for files stored in assets folder is file:///android_asset/*
(with no “s” for assets folder which i was always thinking it must have a “s”).
And, mWebView.loadUrl("file:///android_asset/myfile.html");
works under all API levels.
I still not figure out why mWebView.loadUrl("file:///android_res/raw/myfile.html");
works only on API level 8. But it doesn’t matter now.