Download from this page : http://www.oracle.com/technetwork/database/10204-winx64-vista-win2k8-082253.html
Install and ignore the prerequisite errors about the OS (check MOS note 1173433.1 for details)
Download/install the adequate 10.2.0.5 patchset
Pl identify which version of Windows 7 - only Professional and higher versions are supported. The only 10g software supported on Win 7 is 10.2.0.5 - to download this you will need access to My Oracle Support using a valid Customer Support Identifier (CSI).
MOS Doc 1173433.1 - How to Install Oracle 10.2.0.5 on MS Windows 7 / Windows 2008R2
If you do not have access to MOS, then you are limited to installing 11gR2, which can be downloaded from http://www.oracle.com/technetwork/database/enterprise-edition/downloads/index.html
The Install Guide is here http://download.oracle.com/docs/cd/E11882_01/install.112/e10843/toc.htm
1. C:\dumps\Oracle 10.2.0.4\database\install\oraparam.ini : Change entry Windows=5.0,5.1,5.2,6.0 to Windows=5.0,5.1,5.2,6.0,6.1
2. C:\dumps\Oracle 10.2.0.4\database\stage\prereq\db\refhost.xml: Include a tag for 6.1 also. (Similar to 6.0)
3. C:\dumps\Oracle 10.2.0.4\database\stage\prereq\db_prereqs\db\refhost.xml: Include a tag for 6.1 also.(Similar to 6.0)
It won't let the warning raised and the installation will work fine.