Oracle XE 18 different home location

Oracle XE installed on Windows 7 created a home in HKLM/SOFTWARE/Oracle,
while Toad looking up for available Oracle homes in HKLM/SOFTWARE/Wow6432Node/ORACLE.

How to reconcile that?

You need to get 64 bit Toad to go with your 64 bit Oracle client.

OR - you can install a 32 bit Oracle client to go with your 32 bit Toad.