First of all, a wooden house or anything else that is not conductive cannot make a Farady cage and has no effect on anything of the sort. You're right that a Faraday cage protects fully against electrostatic fields but you should know that it also significantly protects against E&M and you are wrong to say it does nothing, and, no, a Farady cage cannot amplify EMP. And since we're talking about EMP from a nuclear blast there can be a strong electrostatic discharge as well, so the car's cage definitely helps. And when you talk about providing a mesh or a fine screen as protection - that is also a Farady cage, just with finer mesh, the size of which is irrelevant for the electrostatic discharges (a car does just fine), and there's only a very small percentage of the E&M spectrum (a small part of the radio waves spectrum) of EMP that cares about whether it's a mesh or the whole car that is acting as the cage, and for the rest of it (with larger wavelengths) a car's cage is just as good as a fine mesh. Now, I don't know the breakdown of a typical EMP radio wave spectrum by frequencies but assuming it is not preferential to its highest frequency tail (where a mesh would be better) then what I described above is true.