It is possible to abate VOC’s by using an ozone generator. There is a protocol for using an ozone generator which is outlined in the SaferBuilding How-To guide named “Getting Odors out” There is a picture of an ozone generator in that link.
If you’re trying to remove odors from new paint, then there is more than using an ozonator that can be done. You can wash the walls with baking soda and water. Make sure to use a new mop since dirt from a floor mop will likely get your walls dirty. That, and many other methods are discussed in the “Getting Odors out” how to guide mentioned above.
If you have control over the paint, the best solution would be to use the safer paints to start with. While “an ounce of prevention is worth a pound of cure” sounds like a cliché, it fits with respect to not introducing toxins in the first place since it is cheaper than removing them.
SaferBuilding has a how to guide for “Interior Paint” as well which covers more than just the paint itself (caulk, joint compound, spackle, common mistakes, etc.
A final note with respect to moving into a new house or apartment. Paint can be used to cover up a lot of things. If you walk into a newly painted office, house, or apartment and get headaches or otherwise don’t feel well; then don’t count on an ozone generator to make it right. Ozone generators are effective and may well solve the problem, but there could be something else toxic going on that the paint covered up such as mold or pesticide residue. In other words, it wouldn’t be prudent to make a commitment counting on an ozone generator to remove the toxicity.