Can containers that held spoiled food be cleaned and be safe again?

If you can stomach opening the containers and the associated smell, most plastic and glass containers can be re-used with appropriate washing/sterilization.

I would discard the contents, rinse out the debris and scrub out any residue, including removing seals if possible. I would then soak in a 0.25% available chlorine solution (most household bleach is approx 4% available chlorine, dilute appropriately) for 30 min, then rinse the bleach off, wash in warm soapy water and dry. Bleach is very effective against bacterial and fungal contaminants. However, this approach can damage some components of containers, such as rubber seals, so treat with caution. Silicone seals/lids should be fine.

Plastic and glass containers can take up smells from the contents, as can the seals, so it would be worthwhile to give them the sniff test afterwards and see if you can smell any unpleasant smells that might be passed onto food subsequently stored in them.

That's a unpleasant experience to come back to! You can re-use your containers, the hard part is going to be opening them and getting the spoiled food out. I'd suggest doing this outside if you have the space, preferably standing upwind of your garbage bag. A rubber spatula is a good tool for this.

If you have dishwasher safe glass containers they can go into the dishwasher, just rinse them first and put them on the most thorough cycle you have.

Once you have the plastic and non-dishwasher safe containers scraped out wash them very thoroughly in hot soapy water, changing it regularly. Lids can sometimes have a rubbery gasket in them, this should be pulled out if possible so you get at any food behind the gasket and clean the gasket thoroughly. If it won't come out that's fine, don't force it, use an old toothbrush to get in there and get any gunk out (this is a good idea whether there's spoiled food in it or not every once and awhile).

Glass containers won't take on any smells, if you have a smell from a glass container it's because it hasn't been cleaned thoroughly. However, plastic can take on smells from food, even when completely clean. I've tried wiping containers with both a distilled vinegar and a baking soda paste, mostly successfully. Just leaving the containers out and open for a few days has worked as well.