Am i able to save mw3 to my wii so i dont have to have the disk to play the full game?
Is your wii softmodded? Do you have a USB loader?
Yes, you can play MW3 off a hard drive/USB. try looking at the softmod ANY wii guide and the FAT32 guide.
[spoiler=Some Useful Links]
A Basic Introduction to Wii Hacking
Softmod ANY Wii
How To Run & Post A System Check