The best option currently would likely be OwnCloud:
https://owncloud.com/blog/the-android-app-is-here
For syncing just music files Rhythmbox should work.
For Calendar related functions this GPL program can sync calendar
information:
http://dmfs.org/caldav/
Does anyone have recommendations for a TODO application that I can use on
both Replicant and Trisquel? I'd rather it not be hosted by a third party
and I don't mind manually making the sync when I connect my phone (moving
files or whatever).
I already use Tasque and I installed Mirakel,