Staryu is actually pretty fun, although nothing amazing. The best attribute about Staryu is its access to fast Rapid Spin. If you are not planning to use Staryu for that, do not use Staryu. Natural Cure, Recover, and fast Thunder Wave are also pretty nifty as well.
In most of my matches around Staryu, it accomplished the following things: spun away rocks once, did some damage with Scald, maybe paralyzed a Pokemon, and then was sacrificed in order to destroy with my other offensive Pokemon. Staryu does what it needs to do, and not much besides that. Staryu tends to get 2HKO'd by most neutral attacks, but thankfully not many neutral attacks can OHKO it.
Nyara, I've actually considered using Life Orb > Eviolite on Staryu with a moveset of Hydro Pump / Ice Beam / Thunderbolt / Rapid Spin. Staryu isn't very strong, and it would be OHKO'd by practically everything without Eviolite, but at least it can do a bit of damage. The annoying part, however, is that Staryu would have a very hard time using Rapid Spin without dying because of its paper defenses.