I have read so much (dozens of posts) about one thing:
How to unit test business logic code that has Entity Framework code in it.>
If you want to unit test your TaskManager class, you should employ the Repository dessign pattern and inject repositories such as UserRepository or ClientTaskStatusRepository into this class. Then instead of constructing CloseDBEntities object you will use these repositories and call their methods, for example:
User currentUser = userRepository.GetUser(loggedInUserId);
ClientTaskStatus taskStatus =
clientTaskStatusRepository.GetTaskStatus(taskId, clientId);
If yout wanto to integration test your TaskManager class, the solution is much more simple. You just need to initialize CloseDBEntities object with a connection string pointing to the test database and that's it. One way how to achieve this is injecting the CloseDBEntities object into the TaskManager class.
You will also need to re-create the test database before each integration test run and populate it with some test data. This can be achieved using Database Initializer.