"sluttiness" seems to have wide currency nowadays, a lot more than "slatternliness" or "sluttishness". But "sluttiness" is absent from most dictionaries.
I've not heard the first used much at all, Robert, so I can't comment on its wide currency. The second, I've never heard and the third, like many words doesn't have all its potential forms used much.
As regards dictionaries, it's natural that they are "behind the times" for it's people using language who invent words, change their meanings and bring them into more or less frequent use. Dictionaries only catalog these changes.
In the social milieu in which a person would commonly (and I use the word pointedly) refer to a girl as a 'slut', don't expect that his companions would have a vocabulary that includes 'slatten', which would at least expand his vocabulary. I'm surprised that you've even heard 'sluttishness" - you must have read it somewhere.
In Britain, currently, 'slut' is definitely out, and 'slag' is in.
'slut' is possibly still the word in Australia, but it's been a few years since I was there.
If you "Google" for "sluttiness", you’ll find 49700 entries. If you Google for "sluttishness", you get 16200 hits. If you Google for "slatternliness", you get a paltry 4200 hits. This is why I said that "sluttiness" seem to have "wide currency nowadays".
Now looking at the entries for "sluttiness", its usage seems restricted to US English, and to the trendy world of Paris Hilton and the like. Here is from http://blog.searchenginewatch.com/blog/051228-090153:
"December 28, 2005 Using Google To Measure Your Sluttiness A nice find by Nathan at InsideGoogle, Slut-O-Meter lets you find out how promiscuous you are according to Google. It does a search for the words you enter on Google, then searches again using Google's SafeSearch feature, as explained more here. The more the non-Safe results outweigh the safe results, the sluttier you are. Paris Hilton pulls 84 percent. Dick Van Dyke is only 25 percent."