This will prevent the oils from oxidizing, and thus keeping the rags from heating up and igniting. Then have them taken on the hazardous waste collection day in your area.
How to Dispose of Stain Rags Stain, Staining wood
Seal and store in a safe location away from heat and flame.

How to dispose of paint thinner rags. Cover them with water and an oil breakdown detergent. Let them dry, then dispose of them. Here are the proper steps for disposing of paint thinner.
This sludge must be disposed of in accordance with the hazardous waste disposal guidelines in your area. After you recover the clear paint thinner, you will be left with some colored sludge in the bottom of the container. Then, bring this container to a hazardous waste collection site nearest you.
Place them in a metal container with a tight lid, fill with water and bring it to a hazardous waste collection area. You would want to avoid that, right? You can also try to turn in your oily waste disposal container to a hazardous waste disposal event.
Dispose of rags in a sealed metal container. Disposing of used paint thinner. Leave dirty paint thinner to separate.
Dispose of rags in a sealed metal container. Fill the container with water until the rags are submerged. Dispose of the paint sludge.
Place the metal lid tightly over the water soaked formerly combustible rags. Throw away empty paint thinner containers. Dispose of rags in a sealed metal container.
Strain and pour the excess thinner into a glass container and add a label indicating the thinner type and date). Follow these steps to protect your home from fires: What i do in these cases when i am staining with oil based products, i open the rags, drape them over the edge of my trash can, single layer, and other places if i don't care if the stain, or in your case, paint, doesn't matter if it gets around.
So, to summarize, dry out the paint completely, close the lid, toss the can with hardened paint inside safely in the trash. To dispose of rags soaked in paint thinner, you should place them in a tightly sealed metal container, such as a clean paint can, and fill it up with water. Leave dirty paint thinner to separate.
Place soiled and used rags inside and then fill the rest the way with water, seal the top and do not open it. Throw away empty paint thinner containers. This then leaves you with a clean layer on top, that is easier and more manageable to pour.
This can be achieved by keeping the can open in a ventilated room. The easiest and safest way to dispose of flammable oily or solvent soaked rags is to use this method: You can either let them dry out (flattened out, not balled up) or you can throw them in a designated container (usually filled with water) that is designed for these types of materials.
Place the rags in an empty metal container that has a tight metal lid such as an empty paint or stain can. Dont dispose of oily rags or paintbrushes in the trashcan. Contact your local garbage disposal company for their policy on disposal of the can and contents.
Pour the used paint thinner into a glass container (marked with the type of paint thinner and the date), seal it, and let any paint. Rags soaked in paint thinner may combust in air, causing a serious fire. Rags soaked in paint thinner may combust in air, causing a serious fire.
Paint thinner rags are a huge fire hazard and can literally spontaneously catch on fire at any time. Wrap dry thinner and put in trash. If you dont have a sealable container, tear these rags into smaller rags.
Buy a special oily waste disposal can and clean them thoroughly with solvent, then soap and water. There is no need to throw out paint thinner after one use. To dispose of rags properly that have flammable material on them really comes down to two options.
Safely dispose of old paint thinner. That is why learning how to dispose of paint thinner rags properly is crucial for the safety of you and your family. These can be found in your local hardware store.
To help speed up the process, add some sand, newspaper cuttings, sawdust, or a paint hardener. Place them in a metal container with a tight lid, fill with water, and bring it to a hazardous waste collection site. Wrap dry thinner and put in trash.
Rags soaked in paint thinner may combust in the air, causing a serious and dangerous fire. Rags soaked in paint thinner may combust in air, causing a serious fire. Strain, seal, and save used paint thinner for reuse.