For acid/base equilibria I always told my students to focus on the relative stability of the charged species - to me this has always been the most intuitive approach.
For AH
A
- + H
+ more stable A
- means stronger AH acid.
So for Acetic acid vs Oxalic acid I would present a similar argument to yours, compare acetate and hydrogenoxalate and conclude that the -ve charge is more stable in the latter due to 1) induction from the -CO
2H and 2) intramolecular H-bonding to the anion.
For B
+H
B + H
+ more stable B
+H means stronger base B.
e.g. guanidinium vs ammonium