I have a tiny creature occupying the same square as an enemy medium sized opponent. If I use a power with close blast targeting, would it affect the enemy in my square?
No, a close blast power would not affect enemies in the same square as your tiny creature.
From the DDI definition of Blast (emphasis mine):
Close attacks come from the caster's square.
Despite what might sound logical, there is no smaller grid used in D&D4e than 5x5
Close burst powers do affect the square you occupy. They do not effect you unless they specifically says that they do (IE a leader's healing power always specifies).
Area burst powers are ranged, so if you center it on your self (or include yourself in the burst) it will target your square.