First of all: QlikView can be copied to the HD (without installation) and will still run. So running from a USB stick should be no problem.
Secondly: A 32-bit QlikView should run on a 64-bit system without problems.
Thirdly: ODBC can cause problems...
There are two kinds of ODBC, 32-bit ODBC and 64-bit ODBC. Normally, these must match with the QlikView used. E.g. a 32-bit QlikView will by default use a 32-bit ODBC.
However, you can override this by using CONNECT32 or CONNECT64 instead of the default CONNECT in your QlikView script. Then the appropriate ODBC driver will be used.
The 32-bit ODBC is administered using C:\Windows\SysWOW64\odbcad32.exe and the 64-bit ODBC is administered using C:\Windows\System32\odbcad32.exe.