What is one supposed to do with an old hardened esrog (that was used on sukkos) that cannot be burned with the chametz nor is it feasible to be eaten?
Why can’t it be burned with the chametz? Being made of organic matter, I think that even an old and hardened esrog will succumb to the fire (provided the fire is strong enough).
In any case, if this is for some reason not feasable, the esrog can be thrown away. Out of respect, it should be wrapped in a bag before being discarded (although it is permitted to discard the esrog, it is not permitted to cause a bizayon).
It remains preferable to throw the esrog into a strong fire, for instance in a bakery.
See Shut Mahari Weil no. 191; Menoras Ha-Meor, Ner 3, Klal 4, 6:7; Hagahos Maimonion Lulav Chap. 7; Shur Maharshal no. 87; Shulchan Aruch Ha-Rav 448:12; Ben Ish Chai, Vezos Haberacha 8; Mishmeres Shalom Vol. 2 no. 44 sec. 2.