The Google Task list is a service that is available both through GMail and the Calendar, or at the standalone interfaces Google Tasks Canvas or the Hand-Held Device Interface. See screenshots to the right. To synchronize with Outlook using Google Tasks as the "man in the middle", you'll need two applications: one at the iPhone and one at the computer running Outlook.
1. At the Android deviceThere are several tools for Android devices that will let you work with Google Tasks, for example GTasks and Google Tasks Organizer (GTO). I'm using GTask, so that's what I'll be using as an example here. I'm sure there are even more alternatives, but GTasks gets the job done. The free version is ad-based, but you can upgrade for ~$8. That said, the price of GTO is only $3, but it does not have widget support (as of now). A widget is really useful if you ask me. Then you can have the most pressing task list "just a flick away" at one of your home screens. See the screenshot to the right for an example.
2. At the computerHere the only tool I know of is called GogTasks. Incidentally, I'm also the developer of this tool, so a little disclaimer goes out right now ;-) They say that all developing projects starts because the developer wants to "scratch their own itch", and that is also the case here. I needed to get my daily life organized, not forgetting things that needed to get done, and I discovered the lack of a sync tool between Outlook og Google was a hindrance. So I made GogTasks, and this tool will be the second element in getting the iPhone-Google-Outlook-sync up and running.
GogTasks works for both Outlook 2003, 2007 and 2010. You can set it up to synchronize at a regular interval so you basically don't need to worry about it being there at all.
Putting it all togetherAs soon as you've configured GTasks (or GTO) and GogTasks to sync against your GMail account, there's not really much to it. Synchornize your tasks, and they will be available wherever you are - on the bus with your phone/pad, by your work computer with Outlook, or from the internet café in Amsterdam when your there to... visit your aunt.
One thing you should be aware of though, is that Outlook have a much more rich concept of a "Task", with things such as recurring tasks and assigning it to multiple categories. Read about how GogTasks handles that here
The final picture: