You could use the Levenshtein Distance to calculate how much different two strings are amongst themselves. There's some quite complex math there but the actual code is rather short. You can easily rewrite the code in that wiki in Java.
The difference will be measured in integers, saying how many steps you'd take to turn one string into the other. A step may be a character addition, removal, or replacement with another character. It will tell you the amount of steps it takes, but not which steps, nor in which order. But then again, since you only want to measure the total difference, I'm sure that's enough information for your needs.
edit: one of the commenters (kaos) provided a link to an implementation of Levenshtein Distance in the Apache Commons.