You can have one Async Task only and do different things in it by passing a functionality ID, if you may, as a parameter.
Although, I strongly recommend you to create 6 different files, each containing your Async Task class (if they have truly different functionality) and put them in a package "Async Tasks", if you may.
If, for instance, you need to do different sort of requests to a server, you should only have one Async Task, different parameters (such as URL, post parameters, etc) and handle the result different in your onPostExecute method according to the type of request you have done: send an event to your activity that calls the proper method to handle the result.
You can use this technique to manage you more-general Async Tasks