Dear Aswin Kokkat,

You can refer "A Look at the Relationship between the ENSO and the Indian Ocean Dipole " by Ashok et al. (2003), "Impact of the Indian Ocean dipole on the relationship between the Indian monsoon rainfall and ENSO" by Ashok et al.(2001). 

Prof. Ashok Karumuri (University of Hyderabad), Roxy Mathew Koll (Indian Institute of Tropical Meteorology) and Prof. Raghu Murtugudde (University of Maryland) have several contributions in this regard. You can read their papers for a better insight.

The very recent paper is "Teleconnections of ENSO and IOD to summer monsoon and rice production potential of India" by Jha et al.(2016).

Some recent papers are quite critical in this regard like, "Evolution of Indian Ocean dipole and its forcing mechanisms in the absence of ENSO" by  Wang et al. (2016); "Indian Ocean and Indian summer monsoon: relationships without ENSO in ocean–atmosphere coupled simulations" by Crétat et al. (2016); "Statistical Evidence for Asymmetry in ENSO–IOD Interactions" by Lestari and Koh (2016); "The weakening of the ENSO–Indian Ocean Dipole (IOD) coupling strength in recent decades" by Ham et al. (2016).

I am providing links of some other relevant papers.

http://www.sciencedirect.com/science/article/pii/S0377026516300598

http://www.tropmet.res.in/awnew/aw-86.pdf

http://journals.ametsoc.org/doi/abs/10.1175/JCLI3797.1

http://journals.ametsoc.org/doi/abs/10.1175/1520-0442(2004)017%3C3141%3AIACIOE%3E2.0.CO%3B2

I hope this helps.

All the best!

It would be good to analyze the cross-correlation function with different lag times.

you may refer the papers, as advised by the other readers. apart from that some simple analysis you can also perform on your own. take long term data sets of rainfall India (which is available for the past 100 years). ENSO and IOD index are also freely available. At first hand, just perform a correlation analysis. 

You can refer "A Look at the Relationship between the ENSO and the Indian Ocean Dipole " by Ashok et al. (2003), "Impact of the Indian Ocean dipole on the relationship between the Indian monsoon rainfall and ENSO" by Ashok et al.(2001).