32 bit assemblies and dll's cannot be loaded into a 64 bit process and vice versa. You can create assemblies that are "AnyCPU" and those can be loaded into both 64 bit processes and 32 bit processes. Since teh Oracle assemblies are 32 bit, they can only
be loaded into a 32 bit process.
A console app project is by default configured to run in x86 or 32 bit mode. A web application is by default configured in anycpu mode and can thus be loaded into both 64 bit and 32 bit processes.
Either install the 64 bit version of the Orcale client or configure IIS to run in a 32-bit process.