They make great gaurd dogs because of their mate boost and shock torpor damage witch helps protect your raft from leed and sarcos. They also good as body guards because of their speed and the sheer number of them that you can have at once. They can also overwhelm this like mosas and megalodons so you can knock them out in minutes.
Don't ever tame one of those, unless you're trying to get the achievment. Wild ones are very annoying and that makes you think tamed ones will be useful, right? NO, THEY'RE NOT! They do have an aoe attack that stuns, but they're not rideable and the AI won't ever use this attack. Instead, they will keep bitting with a ridiculous damage, like 6 or 7 points.
One of the most feared aquatic wild creatures is totally useless when tamed.
These are passive tames. In my experience trying to tame a 145. You will find having a Basilosaurus will provide you with a mount immune to the shock.
Wear a combination of Riot and Scuba gear. Bring multiple sets. They will destroy your tanks and flippers if you get hit enough times. Lone eels do not deal enough torpor to be a substantial threat with the riot gear.
The hard part is feeding them. They will glow bright blue (without goggles on) when they have built up a charge, and charge you. Discharge a 7 second stun, bite and then flee.
Lure them into an enclosed area. Such as a trap for water tames or a river. This will reduce their mobility and make them an easier tame than in the open ocean. Because they will flee the majority of the tame if they have the room to do so.
-Results of 3/20/17 taming test on Xbox official servers.