Integration Services (SSIS) supports reading data from OData sources. However, there is no OData destination component.
I cannot specify the OData webservice with an HTTP connection manager as web service task in SSIS (i.e. it does not support Windows Authentication).
Using Entity Framework/ASP.NET I think I could just write a post-deployment script. But is there a more straightforward way to update OData (if possible in SSIS)?
I don't think there is an ODATA Destination component created by Microsoft. You can find ODATA Source and create an ODATA connections only. (In SQL Server 2014 you have to install it from the feature pack, in 2016+ it is included).
On the other hand, there is some third party components that you can find in Visual Studio Marketplace:
There was a feature request on Visual Studio website to support ODATA Destination, and it was closed.