I saw a company that sells these short barrel mossbergs and they said all you have to get is a cheap Every Other stamp and I was wondering how you get a permit for a shorty shotgun? can you get one in California?

I'm not sure about California, but as far as the federal laws, AOW is a type of weapon defined under the National Firearms act of 1934 to be a shotgun or rifle made at the factory with a barrel under 18 and 16 inches respectively.  There are some other weapons such as pen guns and others that fall into this category.  The class 3 registration fee for an AOW is $5 as opposed to $200 for a machine gun,sawed off shotgun, SBR, destructive device, and silencer.  In most states it is fairly simple to get one, albeit with about a 4 month wait, but in the Peoples Republic of Kalifornia, there's no tellin' what the laws are.