You have to use the 11g Database Gateway for ODBC (DG4ODBC) to connect from Oracle 10.2.0.4 to Postgres.There's a note on My Oracle Support how to configure the gateway - please have a look at:
How to Configure DG4ODBC on 64bit Unix OS (Linux, Solaris, AIX, HP-UX Itanium) to Connect to Non-Oracle Databases Post Install (Doc ID 561033.1)
I would recommend you to use the latest gateway release (22.214.171.124) which can be downloaded from My Oracle Support portal as well. Just click on Patches and Updates and look for the 126.96.36.199 patch set:
Patch 10404530: 188.8.131.52.0 PATCH SET FOR ORACLE DATABASE SERVER
Although it is a patch set this software can also be used to install the gateway from scratch.
Check out the readme as it lists which ZIP file contains the gateway software you have to download.
The DG4ODBC gateway is for free and its license is included in the Oracle database license. You only need to make sure you have a suitable ODBC driver which is able to connect to your Postgres database.