Classification is the process of organising different organisms in various categories based on their similarities and dissimilarities.
Taxonomy is the process of classifying organisms into various taxa. It includes identification, classification and nomenclature of organisms.
Taxa is plural of taxon. A taxon is any category in the classification system be it kingdom or the species.
Nomenclature is the process of giving an organism a particular name based on a standardised set of rules, so that an organism is known by the same name all over the world.