You need quarter round against all the base as well as the door. Now of course typical Quarter round isn't wide enough so you have to be creative with a build out at the door so the quarter round goes straight thru and covers the gap. What you need here us an oscillating tool, table saw and an air nailer and a tube of painters caulk.

The trick here is building out from the door thresh hold even with the base. A couple of ways of doing it.

You can rip a piece of whatever the width from door threshhold from base to base and carve it around the angled casing or cut the casing with the oscillating tool and slide the buildout under. nail that down then run the quarter round thru.

Sorry if I make no sense. I'm a doer not a teacher. I look at your problem and in my head with my tools it's an easy fix.