To amplify LCAllen's answer:
You can access your Contacts
and Calendar using these apps:
https://play.google.com/store/apps/details?id=org.dmfs.caldav.icloud
https://play.google.com/store/apps/details?id=org.dmfs.carddav.icloud
You can access your email using
these settings:
https://support.apple.com/HT202304
As you are using a non-Apple app
to access your email or other facilities, you are now required to
use an 'app-specific' password in place of your normal iCloud password.
In order to do this you need to set up two-factor authentication for
your Apple ID, and for this you need to have either a Mac running el
Capitan or above, or an iOS device running iOS9 or above.
https://support.apple.com/HT204915
https://support.apple.com/HT204397
If you are unable to set up
two-factor authentication you should set up 2-step verification and use
that to create an app-specific password (see link below) . Then go to
https://appleid/apple.com , select 'Password and Security'; click
'Generate an App-Specific Password' and follow the instructions. Once
you have the password, copy it and paste it into the password field in
the application instead of your usual iCloud password. You should also
keep a note of it (though you can generate a new one if required).
https://support.apple.com/kb/HT204152
You will need to nominate a
'trusted device': any phone capable of receiving SMS messages. There
will be a 2-day wait before you can complete the process.
(A particular caveat (about
2-step only) - you will be issued with a 'Recovery Key' in case you
lose your 'trusted device'. Make sure to write this down and keep it in
a safe place; if you lose both it and your trusted device you will be
permanently locked out of your ID. You'd be surprised at the number of
people who've posted here that they've got themselves into just that
position.)