The work emulation pulled me away from my MAME list.
PS2 - There are no Wii PS2 emulators
GC - The Wii plays GC games by default. You have to install cMIOS and use a backup launcher like NeoGamma to play backups if your drive is capable. Stomp_442 has a guide on here.
DS - DeSmuME is for DS. I cover it in the second part of my emulation guides.