You have another version of the Oracle Client on the Windows 2012 machine. That Oracle Client is not compatible with ODP.NET 22.214.171.124.
In your web.config, you should set your DllPath attribute to point to the location of ORACLE_HOME/bin directory is for your Oracle 126.96.36.199 client. That will likely fix your issue.
If you don't know what DllPath is or how to set it, Chapter 2 is the ODP.NET documentation will tell you how.
For the lazy... it looks something like this in your app.config:
<add name="DllPath" value="c:\oracle\product\11.2.0\client_2\bin"/>
<add name="TraceFile" value="c:\temp\odpnet.trc"/>
<add name="TraceLevel" value="63"/>
<add name="TraceOption" value="1"/>