I modified an existing synchronization tool to synchronize a CalDAV/CardDAV server to a remoteStorage server: https://github.com/untitaker/vdirsyncer/pull/265
I still have to document the usage properly, but I’ve posted a simple config example there to get you started.
CalDAV, for some reason, also supports storing tasks into a calendar (besides events). After you sync those to your remoteStorage server, you can view then with e.g. this task app. It’s rather slow, so it will inevitably hang up your browser for more than 1000 tasks/events. I still have to publish the sourcecode for it and also find a better name.