You could try organizing a "community" garage sale! Pick a date 1 month out from now so they have time to sort and get things ready. Advertise in as many papers/craigslist/street corners, etc so you get maximum attendance (=more junk gone!).
Make it a garage sale contest - the one who makes the most money that day gets a prize (free maid service, cash, or whatever you think they need/want). Or if you can think of a more creative way to get a winner that would be more fair - like a ticket for every item sold, then a ticket drawing at the end of the day. Bonus tickets if you donate the rest of the stuff that you didn't sell - and as for donate, get your truck ready and have everyone load up all the leftovers and do a group donation.
If you don't want to splurge for a prize you might be able to have a maid service or a grocery store donate a gift card if you advertise for them at the sale! Cash prizes are always a huge motivator - if you can afford to do it, is $100 worth your sanity and keeping everyone happy? Plus if you do the group donation you can take the tax deduction.
Make it a party too! Have refreshments, snacks, if it's nice get out the grill and make burgers/dogs (let the tenants eat free but ask for donations from the garage sale shoppers - can't sell food without a permit - so it must be donations). Nice reward for the tenants for participating.
If you have the time, offer to help anyone out that needs help sorting things. Sometimes it just takes someone else to help one see the value in their things. (have you ever watched those organizing shows on TV? if you aren't using it or displaying it - it goes)
There you have it - junk GONE!
Good luck to you!