shadow parasite (HtS 109) reads: Response: After a character's STR is reduced by X, Shadow Parasite gets +X STR until the end of the phase.

the hatchlings' feast (ASitD 50) reads: Any Phase: Kneel 3 influence to choose 3 characters without any attachments. Until the end of the phase, one of those characters gets -1 STR, the second gets -2 STR, and the third gets -3 STR.

do i have the opportunity to trigger shadow parasite 3 times after the event resolves or just once.

You can trigger for each character. Think of it like Joffrey and Valar. There's only one effect doing the killing but multiple triggers for his response.