I have been a Palm OS user for years and had trouble finding a calendar and to do list app on Android that were comparable to Palm's amazing organizing software. I paid for several productivity apps, none of which were quite enough for me. Luckily, I found these free apps that have worked for me.
Astrid (with it's newest updates) is the closest app to Palm's Task List. It has repeating tasks, categories/tags, specific filters, and a few other features former palm users may be used to using. The sorting and filtering functions aren't quite as easy to read as palm and don't work with the widget but the developer replied to my email that they are working to beef this up. I also opened a free rememberthemilk.com account and linked Astrid to it. Rememberthemilk.com is more functional (to me) than the other accounts you can link to Astrid. Did I mention it's free?
I prefer to have shortcuts on my phone desktop instead of the widget. I have a shortcut for sorting by date, and a couple for my frequently used categories/tags. In the main screen that lists all of your sorting and tags lists, simply long press whatever you want to create a shortcut to the desktop.
As for a good calendar app, I would go with Jorte. With it's recent updates, it allows you to have more customized events, like repeating events (which is surprisingly hard to find). You cannot color code events like you could with Palm. However, the many different widget options allow you to pick a widget that will show the event name so you can still do a quick glance at your calendar to know what's coming up without having to click on each day (like you would have to do in the native calendar apps). It can also sync with Google calendar.
As an OCD organizer, I instantly fell in love with Palm's productivity apps. They are easy to use and easy to tailor to your specific needs. While Astrid and Jorte aren't quite as great as Palm, they are the best substitutes out there on Android. Plus, they are free and the developers are quick to respond to questions and suggestions.