The Mad Dog 100% needs an amp it is no where near as sensitive as the 240 or DT770. Maybe going the Shure 840/940 might be a better idea if you don't want to grab an amp as well. Shures though seem to have poor THD ratings on some of their models, which might be the distortion you are hearing.
The Beyerdynamic DT250 might be something to consider now that we realize you might have a hard time amping the Dogs. Its made for production purposes.