How to inject dependencies into the global.asax.cs

The class in your global.asax.cs is your Composition Root, so you can’t (and shouldn’t) inject anything into it from the outside.

However, there’s only one instance of the MvcApplication class, so if you need a service in one of its methods, you can just declare it as a member field – e.g:

public class MvcApplication : System.Web.HttpApplication
{
    private readonly ILogService log;

    public MvcApplication()
    {
        this.log = new MyLogService();
    }

    protected void Application_Start()
    {
        // ...

        this.log.Log("Application started");
    }
}