I'm attacking with a 1/1 Satyr Grovedancer. My opponent blocks with a 1/2 Two-Headed Cerberus with double strike. Does double strike still apply when the creature is blocking? I understand my Satyr will die either way but say it were the case with a 4/4 creature, what would happen?
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Yes, double strike and first strike work while blocking.
Effectively, there is a "first strike combat damage step" in which one set of double strike damage is dealt, and then a normal combat damage step, where all other combat damage is dealt.
So whether attacking or blocking, that phase always occurs, and damage is dealt simultaneously within it.
So in the case of your Grovedancer:
In the case where you attacked with a 2/1 Golden Hind
In the case where you attacked with a 2/2 Travelling Philosopher
In the case where you attacked with a 4/4 Rumbling Baloth
Hope that helps