We donate all sorts of goods every year to places like GRACE and Goodwill. I always use the tax write-off, but if you're giving away a lot of good furniture, you'd probably get more money by selling it than the tax write-off value. You could list your items for sale on Craig's list where the ad is free. I know you're in a time crunch so if you price it cheap enough that it sells quick, you'll get cash from the buyer rather than worrying about how to determine the tax value of anything you give away to charity.
I recently got a flier from a company called "easysale". They supposedly come to your house with a big truck, pick up all the stuff you want to sell, tell you how much they think they can sell it for and then sell it for you on ebay. They obviously take a cut, but you get money and you don't have to be the one setting up the sale. The flier shows their website address as www.easysaleinc.com. I've never used them, nor have I ever known anyone who's used them, but that may be something you'd be interested in vs. a furniture dealer or consignment shop.
If you're just trying to be charitable, however, you can always estimate the value of your items and use those receipts when you file your tax return. I believe there is a limit to how much you can deduct for non-cash donations, however, so keep that in mind if you're getting rid of a lot of high value items. It's best to inventory and photograph the items you donate and talk to a tax professional about how much you can write-off for the items. There are also software programs you can buy, like "deductit" that help you determine the value of the items you donate for tax purposes.
I've given truckloads of things to Goodwill and had The Salvation Army come pick up an entire 2 car garage filled with stuff once after a move. I made a written inventory of everything I gave away and the Salvation Army representative signed it and gave me the appropriate receipt so I'd have it for my taxes. People do it all the time.
It really depends on your ultimate goal. If you need the money, probably best to sell it even if you have to sell it cheaply so you can get rid of it quick. If you're wanting to help someone else out in the process, then a reputable charity would be a great way to get rid of your unwanted items, and you do get a tax benefit to boot.