Some 32 bit software should work, but keep in mind that there are some programs out there that refuse to work on a 64-bit OS, i.e. older or poorly written software. Driver wise, go to Sony's support site and they should give you a list of both 64 and 32 bit drivers that should work with your machine.
Most programs designed for the 32-bit version of Windows will work on the 64-bit version of Windows, with the exception of many antivirus programs. However, keep in mind that device drivers designed for 32-bit will not work on 64-bit computers. Therefore, if you're trying to install a printer or other device that ONLY has 32-bit drivers available, it won't work correctly on a 64-bit version of Windows.