So I'm running Black Ops 2 on my Xbox 360 Slim (250 GB Model). I've not played it in awhile, and just remembered why.
Whenever I join games, whether Online, Private Match, or LAN, what happens is the colors become super bright (almost inverted) and I have no gun but cross hairs. Yes, I can shoot, but when I aim it zooms in like normal, the cross hairs disappear but my gun still doesn't show. When playing with friends my character looks normal from their perspective.
Here's a pic I took on my cell: (Yes it's from snapchat don't mind the text)
This happened to me once, but it was only shades of green and white stripes everywhere(kinda like Tron). Your disc is messed up.... I think you should clean it good. If it is scratched use toothpaste and scrub it good inwards all around the disc(not circles, just rub it from outer layer in all around so it's even). Why? Because toothpaste is an abrasive cleaner witch can help guide the laser over scratches. And make sure after you clean out the toothpaste to use soap and clean out the center of the disc(where you put your finger through) because toothpaste can get stuck in there and is relatively easy to get out.... Then make sure its nice and dry (no soap or toothpaste inside the center) and it should be better(depending on how messed up your disc is) Hoped I helped...
This happens a lot lately on the 360 also. Origins has been un playable with most weapons out of the box having no cross hair or visable weapon.