You were able to manually create the /usr/lib/AntiVir directory, so this does not look like a permission problem.
A "shot in the dark:" I could imagine that Avira's installation script expects the GNU tools to be installed, and that it uses command line parameters for "mkdir," "cp," "install," and "mv" that are unknown to the busybox tools. Do you have the GNU tools (coreutils, and perhaps also util-linux) installed?