1. Visual Studio any version is 32 bit ONLY irrespective of hardware or OS bits. So to DEVELOP with Oracle Client you MUST install 32 bit Oracle ODAC components. Task manager will show devenv.exe *32 (to confirm 32 bit Visual Studio application).
2. You can run your web application inside IIS/IIS Express in your PC which independently can be either 32bit or 64bit. If it is 64 bit, you MUST also install 64 bit Oracle ODAC components which means you'll have to install both 32bit and 64bit in your 64 bit Win7 running on 64bit hardware.
3. In Visual Studio if you compile with "AnyCPU" as target, the resultant binaries (Web/NonWeb) can be both 32bit or 64bit. So if target PC is "AnyCPU" or "x64", you MUST install Oracle ODAC 64 bit in the target OS if that target OS is 64bit. You don't have to install 32bit ODAC in the target PC.
4. One more catch to above scenario is the target OS could be 64bit simulated OS on a 32bit hardware. In such case you MUST install both 32bit and 64bit ODAC components.
So while you ask your network team to download ODP.NET/ODAC Components make sure you ask them to download both 32bit and 64bit. Total nearly 600MB.
Hope this helps many people out there.