Plastic creates humidity which is conducive to mould development and may leave cheese tasting like the plastic it is wrapped in. Blocks or slices of cheese are usually sold wrapped in plastic. Change the plastic for aluminum foil and ensure it is tightly wrapped. Aluminum foil keeps most air out and provides an effective odour barrier. Parchment paper will also do the trick. You should store cheese in a drawer in your fridge so it stays separate from other food. This will help prevent cheese from transmitting or absorbing odour. Finally, remember that shredded cheese freezes really well. It can be added directly to dishes about to be cooked without being thawed first.
I store cheese in plastic wrap or in a plastic bag but mould often forms. There is surely a better way to preserving cheese. Ricardo, what is your best trick?