Sodium chlorite has been used in drilling to control the hazardous gasses released during the process. If you have some air detection equipment you can mix up an activated solution and monitor for levels of chlorine dioxide. The target concentration for inside a house is in the 0.01 - 0.05 PPM range. Here is a recent study done on removing bacteria and virus from school classrooms.
Other studies have demonstrated that chlorine dioxide does remove volatile organic compounds (VOC) from the air, so it should have the same effect on the noxious odors from the oil spill.
Unfortunately, this process is "not ready for prime time," but this is an emergency...
If you don't have the proper equipment to generate and measure the amount of chlorine dioxide in the air, you are at a disadvantage. If you detect the chlorine dioxide odor, you are 10 - 100 times too strong, and chlorine dioxide is a respiratory irritant, so you could end up with more respiratory problems.
A "best guess" effort would be to take a bowl and put 10 ml of 5% sodium chlorite in it and add 10 ml of 6% HCl. Set the bowl as high as you can in the room and walk out. After 10 - 15 minutes, come back in and take a whiff. If you detect the chlorine dioxide odor, the concentration is too high. An additional safety item is that this solution will bleach if it is spilled, so make sure it is sitting on something that won't be effected by its bleaching action, and don't spill. If you do spill, use lots of water to dilute before cleaning up.
Larger rooms may tolerate more, and smaller rooms may require less. The best way to monitor the level is to use air quality meters, but they tend to be a little expensive.
The whole idea is to "scrub" the air of these VOC so your body doesn't have to deal with them.
Another option is to fog the rooms in the house on a regular basis. This is not as effective as using chlorine dioxide gas, but it may help. The fogger solution is made by adding 17 ml of 5% sodium chlorite to 1 liter of water. This will leave a coating on the inside surfaces of the room. This coating will react with odors that come into contact with it and neutralize them. The main safety concern is during the actual fogging process, so be sure to wear your protective equipment during that. Afterward, there is little concern for safety. As odors come into contact with the solution on the surface, they will activate the solution and a very small amount of chlorine dioxide gas will be produced eliminating the odor.
Fogging is usually used in walk in coolers to keep mold, mildew, and odors down. It is applied every 1 - 2 weeks. In a house the load shouldn't be as high so it may be a good starting point to fog once a month.
An interesting analogy for this is like having your dog sprayed by a skunk and then running through your house... every hour. By the way, chlorine dioxide solutions are very effective ways to deal with skunk spray issues too.