To give birth to parasites, do I need to be raped by a jellyfish or a cockroach?
No, you need to get egged from either a Wharfroach, Egg-bee, Egg-fly, or slug, for about 3 times in order for the parasite to change.
You do not give birth to parasites, you just trigger the big parasite scene when not wearing panties when sleeping.
Also, to get parasited, you have to breed with a parasite beast or by random chance of having sex with a bugshroom when at high lewdness.