With bungies, make sure they have sufficient tension to hold. Put several objects together in a bag. Use any bag loops to hold the bungee from slipping off. Use several bungies or an elasticated cargo net.
Hook bungies onto the bottom of the rack legs from the inside, outwards. You can loop the chord between two of the legs then poke the hook out at the bottom. This is more secure than hooking straight from the outside , inwards.
Pannier bags can be expensive. If you want a cheap option check out a mil surplus store fro bags that can be zip-tied to the sides. Respirator bags are a good choice, they are stiff enough to avoid entanglement with the spokes.
You can add some extra stiffenening by rivetting bits of Correx (For Sale signs) inside the bag at the base and inner surface..