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: 
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.
I've had good luck simply storing the cheese tightly wrapped in plastic wrap in the refrigerator. If you use a good quality wrap material and wrap it tightly, the cheese will stay dry and also not lose moisture.

In the past I tried using ziploc bags, evacuating air before sealing, but the simple plastic wrap approach works better. I can keep 6-7 types of cheese fresh during the time it takes my family of four to eat it... up to several months depending on cheese type.