The Madden Julian Oscillation (MJO) interacts with the El Nino Southern Oscillation (ENSO - El Nino/La Nina) to enhance or suppress it. Both the MJO and ENSO are oscillations, but El Nino is a longer wavelength (timeframe) oscillation (running 1-2 years) and tends to be relatively stationary (over the Pacific) while the MJO is shorter (running about 20 days) and travels around the planet on the equator. This means the MJO oscillates between Active and Inactive states while traveling east over the Pacific and over a base ENSO state (be it El Nino, La NIna or neutral). When components of the MJO are in-phase with the same components of ENSO, the MJO can enhance ENSOs impact (or 'constructively interfere' using NOAA terminology). When they are out of phase, the MJO can suppress (or 'destructively interfere') ENSOs effects temporarily. The Active state of the MJO is tracked by it's position on the equator circumscribing the planet. There are 8 positions or Phases, each being 45 degrees in width (roughly 2700 nmiles). Phase 1 of the cycle starts over equatorial West Africa, progressing to Phase 2 over equatorial East Africa to Phase 3 over the mid-Indian Ocean continuing east around the globe until one returns to Phase 1.
For example, assume the current base state of the equatorial Pacific is El Nino. As such, from a wind perspective, the bias is towards westerly anomalies over the entire region (or at least suppressed trades). That means westerly anomalies (or an offshore flow relative to the West Pacific) creates upwelling (cooler than normal water temps, less precipitation and relatively higher pressure) there, and onshore anomalies in the east near the Galapagos, creating downwelling, resulting in warmer than normal water temperatures, enhancing precipitation from the dateline eastward resulting in lower relative pressure. The leading edge of the Active Phase of the MJO produces easterly anomalies and suppresses precipitation, while at it's core, peak precipitation and neutral wind anomalies occur. The trailing edge of the Active Phase produces westerly anomalies and gradually drying conditions.
As the leading edge of the Active Phase moves from Indonesia over the West Pacific (Phase 3-4), it's tendency to create easterly anomalies and suppress precipitation interacts with El Nino's base state, that consists of westerly anomalies and less precip, netting out neutral wind anomalies and dry conditions (i.e. The leading edge of the MJO suppresses the westerly anomalies in the El Nino base state). As the core of the Active State moves over the West Pacific/dateline region (Phase 5-6) precipitation starts building there, driven by the MJO and somewhat by ENSO, and westerly anomalies already in play from the El Ninos base start get enhanced by the MJOs own tendency to create westerly anomalies in the far West Pacific. As the MJO moves east the potential for peak rain moves over and east of the dateline while peak interaction of El Ninos west winds base state becomes enhanced by the MJO's own tendency to generate westerly anomalies (Phase 6-7). Think development of a westerly wind burst in the KWGA supporting Kelvin Wave production. As the Active Phase continues east, peak precipitation potential moves to the East Pacific enhancing the already present precipitation potential being generated by El Nino. And the interaction of MJO westerly anomalies enhances El Nino produced westerly anomalies over the Central and East Pacific (Phase 7, 8), but east of the KWGA, with support for Kelvin Wave production fading. At the same time the Inactive Phase of the MJO starts setting up in the West Pacific, suppressing precipitation over the El Nino base state (which is already suppressing precipitation), and easterly anomalies start interacting with the ENSO westerly anomaly base state, netting out neutral winds anomalies. And the cycle begins again.
The MJO is a short oscillation lasting 20-60 days. It operates on top of an oscillation lasting one year (the Seasons - Fall, Winter Spring and Summer). Likewise El Nino/La Nina are the opposite ends of a 2-7 year oscillation that operates on top of a 15-30 year base cycle called the Pacific Decadal Oscillation (PDO). If you think about it, at any point in time there are 4 oscillations interacting to influence our atmosphere in the form of what we call weather. When the wavelengths line up, the atmospheric effects and influence are amplified. When they are out of phase, weather production is suppressed. It's a carefully orchestrated balancing act all designed to regulate temperature.