This is a bug in this particular version of the Oracle installer. Here is a workaround:
After verifying that the installer is not running, open this file in the staging area where you unzipped ODAC:
.... \ stage \ KIU \ resume \ admin \ cvu_config
And in this file, change the value of CV_ASSUME_DISTID, which is there 6.1
Then save the changes and run the installer again.
This will force the installer to assume that you have Windows 7.
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