Jeff Chace, program director of the institute, said it took about 15 people on Sunday to lug the serpent-like "leviathan" onto shore after it was discovered dead in about 20 feet of water.
"It just amazed me," he said.
Giant oarfish are the longest of the bony fish species -- topping out at around 56 feet in length – but even at 18 feet, a carcass can be a challenge for scientists.
The marine institute is awaiting results of several samples sent out to researchers, including at UC Santa Barbara, but in the meantime, staff members say they lack the capacity to store it.
"This is a once-in-a-lifetime discovery," Chace said.
Institute members are now mulling the fate of the dead fish. One option on the table is to bury it in 3 feet of sand, then let it decompose over a couple of months. After that, the skeleton of the fish would be mounted, and thus preserved.
Giant oarfish are rarely seen, dead or alive. By mounting the skeleton, it would continue to wow staff and visitors alike.
An instructor snorkeling in the waters of Toyon Bay on Sunday stumbled upon the carcass after seeing a "half-dollar-sized eye starting at her from the sandy bottom," Chace said.
The instructor was in 15 to 20 feet of water at the time, he added.
Chace said there were no marks on the oarfish, and it was unclear how it died. Researchers hope to determine more about the animal and how it wound up in Toyon Bay through the samples sent in by marine institute.