Both nairRta and nairRtya are Sanskrit words are derived from another Sanskrit word nirRti. (A not on pronounciation: ai is a dipthong in Sanskrit and Bengali: in Sanskrit the -a- bit is like the -a- in cat, in Bengali it is like the -o- in cold; the R is a sonant r, like what one expresses by the -rrrr- in the onomatopaeic krrrrng, but much shorter). Both nairRta and nairRtya can mean south-western, nairRta is attested earlier (already in the Atharva veda) and has many more senses.
The root R (which also gave as the word Arya; someone who behaves straight, honorable) means to rise, go straight, etc., among many other meanings. nir/nis is a directional prefix with the sense away from or out of, and nir-R is used in the sense of falling or destruction. nirRti, the corresponding noun, means utter destruction, and is the personification of death or corruption already in the Rgveda. The southern direction is associated with death in many of the Indoeuropean cultures, and already in the Atharvaveda the relation between nirRti and the Southern direction are attested. nairRta is Southwestern corner (as is nairRtya), and in Bengali it referred to the break of monsoon which in Bengal appears from the southwest corner (the word in Bengali also continues to mean the southwest corner).
Incidentally, the Sanskrit feminine is NairRtI, NairRta is masculine and neuter.