I'm wondering what are advantages of edmx/csdl over wsdl 2.0 and wadl that Microsoft has choosen it for OData. Any ideas?
Neither WSDL 2.0 or WADL was globally accepted. MS didn't accept any of them.
The way how MS describes OData services is not very fortunate but it is MS strategy. They invested a lot of resources into something called EDM (Entity Data Model) and they now push it everywhere to satisfy their investments. EDMX is just a way to serialize EDM to XML. CSDL is part of EDMX used to describe conceptual model = classes and it is used by MS tools (WCF data services) to pregenerate client side code for you.