From the Rules compendium for when Traits apply.
If the trait modifies the normal procedure for playing that card or another card.
So Ivor's Trait would kick in as the card is played from hand. His discount is applied before A Piece of the Action's discount kicks in. Then A Piece of the Action would further discount Ivor if possible, and set his cost to a minimum of 4.
So if there are 9 Abominations in combination between in Play, and all Boot Hills:
Ivor's Trait reduces his cost to 0. A Piece of the Action Sets a minimum cost of 4. A Piece of the Action did not reduce Ivor's Cost, so you receive no cost reduction on your non-Gadget goods.
You pay 4 for Ivor and full price for your Goods.
If there are 3 Abominations:
Ivor's Trait Reduces his cost to 6. A Piece of the Action reduces Ivor by an additional 2 (because of the minimum of 4).
You pay 4 for Ivor and receive a discount of 2 on your non-gadget goods.
If there is 1 Abomination:
Ivor's Trait reduces his cost to 8. A Piece of the Action reduces Ivor by an additional 4.
You Pay 4 for Ivor and receive a discount of 4 on your Goods.