SOLVED!!
I guess this is a real problem that has not been resolved yet as nobody replied! Neways, I found the solution through hit and trial.
I observed that the library
libx264.so.56 was actually installed but still gave the problem. Some other x264 packages also wanted
libx264.so.56 library. So I removed all of them. But when I did "yum install x264*" they installed the library as well as those packages.
So basically what I found was that the packages could not be installed when the library was there. They got installed when the library was first removed and then installed 'along with them'. The library had to be removed first. Only then the packages installed with the required dependencies automatically then.
Steps:
1. look at my error
2. Remove the 4 packages that needed x264 library
#yum remove libquicktime gstreamer-plugins-bad ffmpeg-libs vlc-core
(Check what all is being removed and mark it)
3. Remove the x264 libraries as well, i.e remove all entries found from "rpm -qa | grep x264". e.g
#rpm -e x264-0-0.10.20070819.lvn8 libx264gtk54-svn20070414_2245-4.fc8
4. yum -y updatel
5. yum install libquicktime gstreamer-plugins-bad ffmpeg-libs vlc-core (and all the other marked packages in step 2)
So with this the system got updated and the libraries+dependencies were also resolved!