The term "natural class" is traditionally used to refer to a collection (class) of sounds that is "natural". When paired with a theory of phonetically-based phonological features, is has been assumed that natural classes are all of the possible conjunctions of features in the right theory of features. For example in the SPE theory of features, the sets [p,t,k], [p,b,m] or [f s θ x v x ð] are natural classes that can be expressed by the feature expressions [-son,-cont,-voice], [+ant,-cor,-cont] and [+cont,-son] respectively. Typically such classes are of interest because phonological rules operate on classes of sounds, in the context of other classes of sounds, and create output classes with some defining property in common. [k,x,q,χ] can be framed as a class in many ways, depending on the theory of features that you assume. In the SPE system, these segments are [+back,-voice] and in certain feature geometric approaches that are Dorsal and voiceless (or just Dorsal, not specified for voicing).
I should point out that to specify exactly [k,x,q,χ] excluding all other possible woulds, you have to specify a lot of other things – [-spread glottis, -constricted glottis, -round, -delayed release, -coronal...] – the exercise of specifying classes of segments using features only makes send in the context of a specific language which has a fixed set of segments to be compared to.