Oracle 10g dump file push into Oracle 11g database
Your problem might very well have to do with incorrect versions or wrong default connection. Make sure that you use the exp utility from the 10g installation and the imp utility from the 11g installation.
Also make sure that the environment variables like ORACLE_HOME are correct and that PATH is adjusted for the correct ORACLE_HOME/bin

How does your connect string look like?
Is your TNS_ADMIN variable defined? (if not, you might need to have multiple tnsnames.ora files in place, or tnsnames.ora is in a platform specific location (/etc, /var/opt/oracle etc.)) tnsping shows where it gets the sqlnet.ora (next to tnsnames.ora) from.

Even better is to start using expdp and impdp. You can use impdp to directly import your data in the 11g database, using a datasbase link.