Classification/Nomenclature of aroma and flavour compounds - terpenes, aldehydes, and alcohols, etc
Perhaps by classification/nomenclature you are referring to odour descriptors. If I remember correctly I have already covered a similar question about possibility of defining smell, so I will extract relevant parts here:

Odour descriptors and odour profiles

Odour descriptors are the words that come to mind when smelling a substance.
The more generally understood the words are, the more useful they are as descriptors. In practice, it is easy for any observer, after a little training, to use the standard descriptors of fragrance chemistry. Example of descriptors include musky, camphoraceous  etc

Smelling chemical groups

A fact that has, in our opinion, received too little attention from olfaction researchers is the ability of humans to detect the presence of functional groups with great reliability.

The case of thiols ($\ce{-SH}$) is familiar, but groups ($\ce{NO2}$), aldehydes ($\ce{C=O(H)}$), can be reliably identified once the odour character the functional group character confers is known. When nitriles are used as chemically stable replacement for aldehydes, they impart a metallic character to any smell: cumin nitrile smells like metallic cumin (cuminaldehyde), citronellyl nitrile smells like metallic lemongrass (citronellal), and nonadienylnitrile smells like metallic cucumber (nonadienal). Oximes give a green-camphoraceous character, isonitriles a flat metallic character of great power and unpleasantness, nitro groups a sweet-ethereal character,etc.

Here are some odour categories and their representative molecules, chosen to illustrate
structural diversity:

Musk


  Musk odour descriptors might be “smooth clean, sweet and powdery”. The
  molecules that possess this odour character are exceptionally diverse
  in structure. Macrocyclic musks contain a 15-18 carbon cycle closed
  either by a carbonyl or by a lactone and smell similar but fresher and
  more natural, often with fruity overtones (cyclopentadecanolide,
  ambrettolide). Nitro musks, discovered originally as a byproduct of
  explosives chemistry, smell sweeter and are reminiscent of
  old-fashioned barbershop smells.




Representatives from five chemical classes which yield musk odors. 1 androst-16-en-3a-
ol, a steroid musk. 2: ambrettolide, a macrocyclic musk. 3: Musk Bauer, a nitro musk. 4: Tonalid, a
tetralin musk. 4: Traseolide, a indane musk.

Ambergris


  Originally derived from concretions spat out by whales and aged in the
  sun, ambergris odorants smell nothing like natural ambergris tincture,
  which has a weak animalic marine smell. The smell of ambergris
  odorants was once aptly described to us by a chemist-perfumer as
  “glorified isopropanol”. Ambergris odourants provide an interesting
  combination of very closely related smells with widely different
  structures: amberketal, timberol, karanal and cedramber




Two ambergris odorants, timberol (left) and cedramber (right)

Bitter almonds

This easily-recognized category is interesting  because it includes a small molecule (HCN) which, however, is perceived by a large fraction of observers  to smell as metallic not almond-like to. Benzaldehyde, nitrobenzene,trans-2-hexenal (but see above) are good examples.



Green


  Cut grass, fresh green bean notes with a sharp, almost aggressive
  feel. Diverse compounds possess this descriptor, ranging from classic
  grassy notes of cis-3-hexenol and ligustral, to the cucumber peel of
  nonadienal and the bell-pepper green note of some pyrazines.




Some examples of green odorants. Clockwise from top left cis-3-hexenol, ligustral, nonadienal and ethylmethoxypyrazine.

Camphoraceous

Camphor, cyclooctane, cineole are good
examples of camphoraceous smells, and smell rather similar to each other.



Three camphoraceous odorants: 1,8 cineole, camphor and cyclooctane

None of the above 


  Many other categories such as musty, spicy, aldehydic, lactonic,
  indolic, marine, etc exist, each with subdivisions. It must be
  emphasized that the odor categories above are merely convenient
  descriptors and only cover a very small fraction of odor “space”. In
  fact, particularly when one steps out of perfumery materials proper
  into smells noticed by chemists in the course of organic and inorganic
  syntheses the most frequent descriptor appears to be sui generis, i.e.
  a smell associated with nothing in particular


The complexity of structure-odour relations, and the fact that the three dimensional structure of the receptor site is unknown, make it very difficult to apply conventional quantitative structure activity relationships. For detailed SAR and theories please refer to above linked post.

References

Structure-odour relations: a modern perspective: Luca Turin et al