I'm going to give you the answers from what I've just went through on Windows Server 2008 R2 which is a 64 bit operating system. The application suite of libraries I was given were developed using .net 3.5 x86 with the older DLL libraries and I was stuck because I had installed the newer x64 clients from oracle.
What I found was the following: Install the latest x64 client from Oracle for Windows Server 2008. I believe this would be the 2.7.0 client. When you select the installation, make sure you do custom and select the .NET libraries. Configure your tnsnames files and test your tnsping against your data source.
Next, if you are running a 32 bit application, install the same version of the client for 32 bit. Also, follow the same installation routine, and select the same home.
When your finished, you will find that you have a single app/product with two client directories (Client1 and Client2).
If you navigate to the windows/assemblies directory you will find that you have a reference to the Oracle.DataAccess.dll (x2) with one for x86 and one for AMD64.
Now, depending on if you have developers or are developing on the machine yourself, you may be ok here, however, if they are using older drivers, then you need to perform one last step.
Navigate to the app\name\product\version\client_1\odp.net\publisher policy\2.x directory. Included in here are two policy files. use gacutil /i to install the Policy.2.111.Oracle.DataAccess.dll into the GAC. This will redirect legacy oracle ODP calls to the newer versions. So, if someone developed with the 10g client, it will now work with the 11 client.
FYI -- Some may be installing the latest ODP.NET with the 2.111.7.20. The main oracle client itself comes with 2.111.7.0 .. I've not had any success with the 7.20 but have no issues with the 7.0 client.