How do I export data from Oracle 11.1 to 10.1?
To do this, you'll be wanting to use the 11.1 Data Pump (expdp/impdp) rather than exp/imp. With Data Pump you export using the higher version export utility with the VERSION= parameter.

For example:

expdp scott/tiger version=10.1 directory=DUMPDIR dumpfile=DUMPFILE.dmp logfile=DUMP.log

Don't forget to create the directory (using CREATE DIRECTORY DUMPDIR AS '/path/to/dir';) first.