Octopi is the oldest plural form of octopus, coming from the belief that Latin origins should have Latin endings. However, octopus is not a simple Latin word, but a Latinized form of the Greek word októpus. Consequently, its “correct” plural form would logically be octopodes.

Nowadays "octopodes" and octopuses" are both acceptable, the latter being more regularly used.

"Squid" on the other hand isn't Latin or Greek, of unknowns origin, probably from a sailor's variant of "squirt"; late 15c., squirten, squyrten "to spit water from the mouth" (intransitive), a word of uncertain origin, perhaps via Middle Dutch or Middle Low German, probably ultimately imitative.