Question: Just like it says in the title, how can I store blocks of cheese for max shelf life? I will be making a grilled cheese sandwich and shredding 3 varieties of cheese (cheddar, swiss, parm(?)) and I am afraid that I won't be able to use three whole blocks on one sandwich.

Answer: 
Hard, aged cheeses like cheddar and Parmesan are fine to freeze, particularly if you're going to be melting them when you get around to using them anyway. Freezing causes ice particles to break up the molecules of the cheese, and when they thaw, they leave holes in what was (prior to freezing) a pretty smooth cheese. So you might notice if you freeze blocks of cheese, they are more crumbly when you unfreeze them than they were when you bought them. The cheeses you're working with should be fine if stored properly, but softer / creamier cheeses (brie, harvarti, etc.) might become somewhat unpleasant if you freeze them.

As far as storage is concerned, you can actually do one of two things:

1. Grate the cheese before you freeze it. All you need to do for this method is grate your cheese and put it in a ziploc freezer bag (thicker than a regular zip-top bag). Just make sure to squeeze the air out before sealing, and seal it well.
2. Freeze the cheese in blocks. Wrap them in plastic wrap and then put then in a ziploc bag, and you should be all set; it'll keep for 4-6 months. ([source](http://food.unl.edu/web/fnh/food-facts#canufreeze))

No matter which method you use, you may notice a slight change in texture. Make sure you thaw the cheese before using it. (Though I've put frozen shredded mozzarella on pizza and frozen shredded Mexican cheese blend - a blend of cheddar, monterey jack, queso blanco and asadero - on tacos and not had any trouble.)
The best way to keep cheese in the fridge ... and the way I've made semisoft cheeses like cheddar last 6-10 weeks, sometimes more:

1. Wrap the cheese in butcher paper, or baking parchment if you can't get butcher paper.
2. Enclose the wrapped cheese in a plastic grocery bag or plastic wrap.
3. Each time you slice off some of the cheese, change the paper.

The paper keeps the cheese dry, and the plastic keeps it moist. So the cheese doesn't dessicate, but doesn't get moldy either. Works a charm.