I'm not sure LD_LIBRARY_PATH has anything to do with the direct loading of ODBC.so as the full path to it will be specified when the DynaLoader attempts to load it. More likely is that ODBC.so depends on something else that the dynamic linker cannot find. Try running ldd on /usr/lib64/perl5/site_perl/5.8.8/x86_64-linux-thread-multi/auto/DBD/ODBC/ODBC.so as root and non root users to look for a difference. You may need to add a path to say unixODBC libs etc to your dynamic linker configuration - see man ld.so. For example, on my machine:

$ ldd /usr/local/lib/perl/5.10.0/auto/DBD/ODBC/ODBC.so
    linux-gate.so.1 =>  (0x00694000)
    libodbc.so.1 => /usr/lib/libodbc.so.1 (0x00a87000)
    libc.so.6 => /lib/tls/i686/cmov/libc.so.6 (0x00223000)
    libltdl.so.7 => /usr/lib/libltdl.so.7 (0x003ad000)
    libpthread.so.0 => /lib/tls/i686/cmov/libpthread.so.0 (0x00f3e000)
    /lib/ld-linux.so.2 (0x00d18000)
    libdl.so.2 => /lib/tls/i686/cmov/libdl.so.2 (0x00567000)
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One last thing to check is whether you are running SELinux.