Anytime you cook food, it releases small oil droplets into the air. That is why the food odor can be sensed throughout the house. Over time the oil collides into dust in the air which will eventually weigh the oil down and cause it to fall to the ground or stick to something. That is why dust sticks...and can't just be blown away...you need to wipe it away.
In order to get rid of the smell, you need to clean up the mess as much as possible and that would extend to dusting and vacuuming, almost every surface in the home. You probably need to even wipe down everything you can too.
Over time, the grease will break down by itself but that all depends on how much you have spread throughout the house.
Air fresheners typically only mask the odor, or will trick your nose into not smelling the odors, but for these to work they have to come in contact with the grease source. Most air purifiers release ozone that works wonders on odors, but scar your lung tissue (If you get an air purifier, find one that doesn't release ozone.)
To accelerate the breakdown of the grease, you may be able to find some good enzymes. This will just help to remove the source quickly. You would spray these enzymes like fabreeze (in a little spray bottle), or you may be able to find a company that can fog your home with them.
My company cleans up old restaurants that have a stale grease smell, and after we fog them with enzymes patrons and the employees can always tell a huge difference.
I hope this helps you.