Android: Back in April, Microsoft announced plans for an Android Outlook client replicating its Office Web Access interface. That app is now available in a preview version, but only some accounts will be able to test it.
To test the release, you'll need to have an Office 365 business account -- Exchange accounts, Office 365 home and personal and Outlook.com aren't yet supported. Your device also needs Android 4.4 and a regular-sized screen (that is, the app won't work on tablets).
The app has feature equivalence to the existing iOS release, which means it offers a mobile-friendly version of the web OWA interface. It also offers auto-syncing of contacts with your OWA account. The final version is expected later this year.
OWA for Android now available on select devices [Office Blogs]