The Abaia is described as a giant eel that lived in the bottom of the fresh water lakes of the Solomon, Fiji and Vanuatu Isles. This supposedly magical eel was very protective of the fish and other defenseless critters it lived with. Some say this is because it saw the fish as it's children and any creature that dared to harm or disturb them was immediately overwhelmed with a large wave, caused by the Abaia's powerful tail, thrashing underwater. In the case of humans, this was usually fatal for humans because it sank the ship they would fish from. Though perhaps the eel was protective of its food source or habitat rather than the fish. It could be wary of itself also. Superstition goes farther to claim storms caused by this creature.
In another form of this story, the Abaia causes a great rain to flood the lake and kill anyone who harms or disturbs it's children or itself. An example of this is in the following Melanesian story:
He caught many fish and returned the next day with the people of his village whom he had told of his discovery, and they also were very successful, while one woman even laid hold of the great eel, Abaia, who dwelt in the depths of the lake, though he escaped her.
Abaia was now angry at the village people, for his fish had been caught and he, himself had been seized, so he caused a great rain to fall that night, and the waters of the lake also rose, and all the people were drowned except for an old woman who had not eaten the fish and saved herself in a tree.
I would personally classify this creature as both a cryptid and a mythological one. The main reason is based on the legend of the giant octopus and giant squid, which has been proven real. Is it that far fetch to think that a giant eel somehow had access to the lakes from the sea at one point of time? Perhaps it got trapped in the lakes or perhaps it chose to inhabit the lakes. Though it is doubtful it had any weather controlling powers, the people feared this creature. It made for great stories.
Citing:
https://en.wikipedia.org/wiki/Abaia
http://mythicalcreatureslist.com/mythical-creature/Abaia
http://cryptidz.wikia.com/wiki/Abaia
Picture:
http://3.bp.blogspot.com/_iPk_gp0vW80/TLmbAKSbOHI/AAAAAAAAAC0/gQQJcUVS7fs/s1600/eel-3-final-small.jpg
https://www.theguardian.com/world/2015/may/14/giant-conger-eel-caught-plymouth-fishermen