Solubility of NOx gases
$\ce{NO_x}$ can be quantitatively removed from such combustion streams by absorption/dissolution in basic aqueous solutions containing an appropriate oxidizing agent. While $\ce{NO2}$ is readily soluble in aqueous solution, $\ce{NO}$ is not. However, $\ce{NO}$ is easily converted to $\ce{NO2}$ when an oxidant is added to the solution.  

The PhD thesis by Chen-Lu Yang at NJIT, "Aqueous Absorption of $\ce{NO_x}$ Induced by Sodium Chlorite Oxidation", concluded the following:  


$\ce{NO2}$ is essentially quantitatively absorbed in $\ce{NaOH}$ aqueous scrubbing solutions.  
$\ce{NO}$ is not absorbed by $\ce{NaOH}$ aqueous scrubbing solutions.  
$\ce{NaClO2}$ containing aqueous scrubbing medium quantitatively oxidizes $\ce{NO}$ to nitrate [which is highly water soluble].  


The net effect of these solubility/reactivity properties is that $\ce{NO}$ and $\ce{NO2}$ can be quantitatively removed from a gas stream using an aqueous solution of $\ce{NaOH}$ and $\ce{NaClO2}$  

Additionally, according to this PubChem entry, $\ce{NO}$ is soluble in sulfuric acid, ethanol and carbon disulfide, while according to this Wikipedia article, $\ce{NO2}$ is soluble in carbon tetrachloride, nitric acid and chloroform.