How does El Niño affect thunderstorm/tornado/CAPE activity in the central United States?
According to the NOAA document A Comparison of Rawinsonde Data from the Southeastern United States during El Niño, La Niña, and Neutral Winters (Sankovich et al.) report that


  Schaefer and Tatom (1998) considered
  the number of tornadoes per year in the United
  States and sea surface temperatures (SST) in
  various portions of the Pacific Ocean to try to
  discern an impact of ENSO on the occurrence of
  tornadoes. Their statistical inquiries showed no
  major influence, but their data does show a signal
  that more tornadoes tend to occur in the mideastern
  states during the La Niña phase.


However, another study cited by Agee
and Zurn-Birkhimer (1998) state


  that tornado
  occurrences do not favor one ENSO phase but
  rather exhibit a shift in geographic location. For
  example, their results suggest that more
  tornadoes occur in the lower Midwest, Ohio Valley,
  Tennessee Valley, and mid-Atlantic region during
  the La Niña phase than in any other phase.


This is further concluded by Bove (1998) concluded that


  increased tornado activity over
  the Ohio and Tennessee River Valleys during the
  cold La Niña phase.


Sankovich et al. conclude that


  Like all climatological signals, they [ENSO]
  represent long-term trends. They do not provide a
  tool for making seasonal or other extended
  forecasts; rather, they show that other things being
  equal, the atmospheric stratification over the
  Southeastern United States is typically less
  compatible for the occurrence of severe
  thunderstorms (3/4” or larger hail, thunderstorm
  gusts of 58 mph or faster, tornados) during a La
  Niña winter than during Neutral or El Niño winters.


In the paper A seasonal-scale climatological analysis correlating spring tornadic activity with antecedent
fall–winter drought in the southeastern United States (Shepherd et al. 2009), state that to 


  remove the uncertainty
  associated with the ENSO debate, we consider a new approach
  by focusing on antecedent drought conditions for a region.


Whereby, they conclude that the relationship between drought and incidences of tornadic and severe thunderstorm behaviour to possess a


  statistically significant tendency for
  fall–winter drought conditions to be correlated with below-normal tornado days the following
  spring in north Georgia (i.e. 93% of the years) and other regions of the Southeast. Non-drought
  years had nearly twice as many tornado days in the study area as drought years and were also
  five to six times more likely to have multiple tornado days


References:


Schaefer, J. T., and F. B. Tatom, 1998: The
relationship between El Niño, La Niña, and
United States tornadoes, Preprints, 19th Conf.
on Severe Local Storms, Minneapolis, MN,
Amer. Meteor. Soc., 416-419.
Agee, E., and S. Zurn-Birkhimer, 1998: Variations
in USA tornado occurrences during El Niño
and La Niña, Preprints, 19th Conf. on Severe
Local Storms, Minneapolis, MN, Amer.
Meteor. Soc., 287-290.
Bove, M.C., 1998: Impacts of ENSO on United
States tornadic activity, Preprints, 19th Conf.
on Severe Local Storms, Minneapolis, MN,
Amer. Meteor. Soc., 313-316.