I love to use cardboard and other trash as building material, and you get a way more interesting story when people ask: "What is is made of?" And you can answer: "You know, what ever I had that day, pizzaboxes and a soda can..."
So even though you will not get the most resilient costumes, this is a handy way to get some cheap costumes.
Splicer masks are very popular, here is a way to make those.
And for Genki I made a "dragon scale" chest armor.
An elvish pauldron is never wrong, here is a way to use fabric to cover up the cardboard.
Even helmets can be made out of cardboard and other bits, here is Dovahkiin iron helmet from Skyrim.
To make more organic forms paper clay can be your solution. This clay air dries and can be painted sanded and carved when dry. I buy mine from Clas Ohlson.
And with this clay you can make staffs like these:
Sea Goddess - Kraken staff
Death elf - Skull staff