Styx are cheesy as hell and I don't listen to them by choice but I still enjoy enough of their songs (mainly "Come Sail Away" and "Mr. Roboto") to prevent me from ever considering them a truly shitty band. Not a fan of the Backstreet Boys song (or any of their stuff really) but I guess it's catchy enough. Good rule of thumb with that type of music is, if you're someone who dances and the song comes on at a party or in a club, do you dance? If so, the song/artist can't really be called shitty because they've served their purpose.
Not familiar enough with the other songs/artists you mentioned to really have an opinion one way or the other but I do really dislike the song "Bad Company".