You don't get in until you have collected all of the five sacred items. After that Hercules is convinced to help you and he smashes the gate open.
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When you convince Hercules he smashes the lock for you
I'd just use a walkthrough because there to much stuff to write on this plus you get to know what order to things in.
how do you get the red rose on mythology island from poptropica?
After you have the Hades Crown and the Trident from Poseidon, use the mirror to travel to the gate of Olympus (lightning bolt symbol at top). Hercules will smash open the lock and you can enter Olympus.
You do what the sphinx wants!