How will global warming affect climate systems like the ENSO or the MJO?
Still undetermined, though a number of papers on the subject suggest global warming will increase the variance in both of the climate systems you mention. They suggest more research and more refined models are needed to narrow down the uncertainties.

Some definitions:


  The Madden-Julian Oscillation (MJO) is the major fluctuation in
  tropical weather on weekly to monthly timescales. The MJO can be
  characterised as an eastward moving 'pulse' of cloud and rainfall near
  the equator that typically recurs every 30 to 60 days. (Australian Bureau of Meteorology)
  
  The El Niño/ Southern Oscillation (ENSO) cycle refers to the coherent
  and sometimes very strong year-to-year variations in sea- surface
  temperatures, convective rainfall, surface air pressure, and
  atmospheric circulation that occur across the equatorial Pacific
  Ocean. El Niño and La Niña represent opposite extremes in the ENSO cycle. (National Weather Service Climate Prediction Center)


El Niño is the "warm phase" of sea-surface temperatures in the east-central equatorial Pacific with a variety of effects on regional and global weather. La Niña is the "cold phase" of the oscillation.

One of the predictive challenges is that climate change is not monotonic. It's generally held that will be a "warmer-get-wetter" impact -- warmer oceans produce more evaporation and therefore more precipitation. But ocean states are also affected by highly complex relationships involving currents and convection.

Here are extracts from the abstracts of a couple of recent papers on the subject(s) (actual papers are paywalled):

In Intermodel Uncertainty in ENSO Amplitude Change Tied to Pacific Ocean Warming Pattern, Zheng, et.al. compare actual sea-surface temperature measurements to the outputs of various models and write:


  To the extent that correcting model biases favors an El Niño–like mean
  warming pattern, this study suggests an increase in ENSO-related SST
  variance likely under global warming.


In The MJO and global warming: a study in CCSM4, Subramanian, et.al, write:


  The RCP8.5 run exhibits increased variance in intraseasonal
  precipitation, larger-amplitude MJO events, stronger MJO rainfall in
  the central and eastern tropical Pacific, and a greater frequency of
  MJO occurrence for phases corresponding to enhanced rainfall in the
  Indian Ocean sector. These features are consistent with the concept of
  an increased magnitude for the hydrological cycle under greenhouse
  warming conditions.


In MJO Intensification with Warming in the Superparameterized CESM, Arnold, et.al. said their modeling runs showed "Intraseasonal precipitation increases at a rate of roughly
10% per 1 K of warming, and MJO events become 20%–30% more frequent," but conclude:


  This work adds to existing evidence that MJO activity may increase in
  response to global warming. Evidence for an MJO dependence on SST has
  been identified in observations (Hendon et al. 1999; Slingo et al.
  1999; Jones and Carvalho 2006; Oliver and Thompson 2012), and in some
  numerical models (Lee 1999; Caballero and Huber 2010; Arnold et al.
  2013; Schubert et al. 2013). However, other models have shown negative
  or neutral trends with SST (Takahashi et al. 2011) or a strong
  dependence on the spatial pattern of warming (Maloney and Xie 2013),
  so any conclusions regarding future trends should be viewed as
  tentative.