If its wood, try baking it in an oven. I've heard everything from 300F for 3 hrs down to 200F for 30min. You could search around online for something more definitive. Just keep an eye on it so it doesn't burn your house down.
I've heard of soaking in bleach water, again the length of time and strength of the solution varies. I've heard 1 part bleach to 10 parts water, which seemed strong to me. I've also heard a cap or two for a bucket. Bleach is some strong stuff. In this case, rinse thoroughly, and maybe some hours of soaking in plain water afterwards wouldn't be a bad idea depending on how much bleach soaks into the item. I've had some items that even after hours of soaking reeked of bleach and I won't put anything that smells like bleach near my animals. I try and reserve bleaching for serious events, such as mites.
For other cleaning, I've ran food items through the dishwasher without detergent. The booster heater in there is to sanitize your plates, so I figure it will sanitize, at least the surface, of the cage furniture.
You could also wash, scrub, and soak in hot water with a mild detergent, again rinsing thoroughly afterwards.
I feel the best about the dishwasher and baking approaches because they avoid any variety of chemicals. Along those lines, I've heard of people pouring boiling water over their cage decorations.
I personally have never used vinegar, so I cannot comment on that.
The other option is try and avoid porous furniture.
