I am about to purchase a house that was damaged in a fire and sitting for 4 years. The fire was mostly contained to a small area, but some joists were burned quite badly, while other just had some discoloration. I'm going to be putting in new joists, but I wanted to see if it was best just to sister up to the existing badly burned joists or if would be be better to remove them altogether? There is no smoke smell from anything since it's been sitting for so long, and I couldn't think of any way that the burned joists could damage the new joists, and I figured that as long as they didn't cause any damage to the new joists, they just provide some extra strength so it seemed better to leave them, but wanted to check my logic.
As a home inspector, I can tell you that sheer existence of those damaged joists are going to be a RED FLAG at any time you decide to sell and move on. If they are badly burned, they are not structurally sound and should be removed. Install a few temp supports on ends of adjacent joists, then remove and replace them one or two at a time. Use proper joist hangers, proper intervals and upgrade the size if current code requires. I little more work now will pay off big for you later. The cost will not be much different, just a bit more labor.
Fine if you leave them just consider covering burner or smoked wood with a kilz primer for no after smell or effects.