I don't have vault on server. I'm using CraftBukkit 1.5.1-R0.3 and Essentials-Pre2.11.1.2 (hook is on).

2013-05-02 02:10:48 [INFO] KodekPL issued server command: /v
2013-05-02 02:10:48 [INFO] [VanishNoPacket] KodekPL reappeared.
2013-05-02 02:10:48 [SEVERE] Unhandled exception executing command 'v' in plugin VanishNoPacket v3.17
org.bukkit.command.CommandException: Unhandled exception executing command 'v' in plugin VanishNoPacket v3.17
at org.bukkit.command.PluginCommand.execute(PluginCommand.java:46)
at com.earth2me.essentials.Essentials.onCommandEssentials(Essentials.java:335)
at com.earth2me.essentials.Essentials.onCommand(Essentials.java:320)
at org.bukkit.command.PluginCommand.execute(PluginCommand.java:44)
at org.bukkit.command.SimpleCommandMap.dispatch(SimpleCommandMap.java:189)
at org.bukkit.craftbukkit.v1_5_R2.CraftServer.dispatchCommand(CraftServer.java:545)
at net.minecraft.server.v1_5_R2.PlayerConnection.handleCommand(PlayerConnection.java:980)
at net.minecraft.server.v1_5_R2.PlayerConnection.chat(PlayerConnection.java:896)
at net.minecraft.server.v1_5_R2.PlayerConnection.a(PlayerConnection.java:841)
at net.minecraft.server.v1_5_R2.Packet3Chat.handle(Packet3Chat.java:44)
at org.spigotmc.netty.NettyNetworkManager.b(NettyNetworkManager.java:186)
at net.minecraft.server.v1_5_R2.PlayerConnection.d(PlayerConnection.java:110)
at net.minecraft.server.v1_5_R2.ServerConnection.b(SourceFile:35)
at org.spigotmc.MultiplexingServerConnection.b(MultiplexingServerConnection.java:72)
at net.minecraft.server.v1_5_R2.MinecraftServer.r(MinecraftServer.java:582)
at net.minecraft.server.v1_5_R2.DedicatedServer.r(DedicatedServer.java:223)
at net.minecraft.server.v1_5_R2.MinecraftServer.q(MinecraftServer.java:471)
at net.minecraft.server.v1_5_R2.MinecraftServer.run(MinecraftServer.java:403)
at net.minecraft.server.v1_5_R2.ThreadServerApplication.run(SourceFile:573)
Caused by: java.lang.NoClassDefFoundError: net/milkbowl/vault/chat/Chat
at org.kitteh.vanish.hooks.plugins.VaultHook.whatsInTheVault(VaultHook.java:40)
at org.kitteh.vanish.hooks.plugins.VaultHook.getPrefix(VaultHook.java:20)
at org.kitteh.vanish.VanishAnnounceManipulator.injectPlayerInformation(VanishAnnounceManipulator.java:98)
at org.kitteh.vanish.VanishAnnounceManipulator.fakeJoin(VanishAnnounceManipulator.java:119)
at org.kitteh.vanish.VanishAnnounceManipulator.vanishToggled(VanishAnnounceManipulator.java:153)
at org.kitteh.vanish.VanishManager.toggleVanish(VanishManager.java:190)
at org.kitteh.vanish.VanishCommand.onCommand(VanishCommand.java:45)
at org.bukkit.command.PluginCommand.execute(PluginCommand.java:44)
... 18 more
Caused by: java.lang.ClassNotFoundException: net.milkbowl.vault.chat.Chat
at java.net.URLClassLoader$1.run(URLClassLoader.java:366)
at java.net.URLClassLoader$1.run(URLClassLoader.java:355)
at java.security.AccessController.doPrivileged(Native Method)
at java.net.URLClassLoader.findClass(URLClassLoader.java:354)
at org.bukkit.plugin.java.PluginClassLoader.findClass0(PluginClassLoader.java:87)
at org.bukkit.plugin.java.PluginClassLoader.findClass(PluginClassLoader.java:53)
at java.lang.ClassLoader.loadClass(ClassLoader.java:423)
at java.lang.ClassLoader.loadClass(ClassLoader.java:356)
... 26 more

Write one version of Vault support, upload another. Oops. I'll have 3.17.1 out soon. In the mean time since you're still on 1.5.1 you can use the previous version.

Fixed in 3.17.1 (AND I TESTED!)