How is electro-magnetic wave formed without medium? There are particles in a medium. When these particles oscillate with SHM motion, a flow is formed. That is called a wave.
But when there is no medium, there is no oscillation. That means no flow. Eventually no wave! 
But electro magnetic wave is formed without any medium. How is it possible?
Again so many said,"EM waves are the oscillation of EM field. " Oscillation of particles mean "particles are getting down and up continuously". Then what does "oscillation of EM field " mean?
 A: The classical waves like sound do need a medium to travel, you are right.
In the early times, electricity and magnetism were thought to be separate, and they came together in Maxwell's equations, and were describing the classical EM wave and its propagation.
As we were figuring out a way to describe the micro level (QM), we had to use quantum electrodynamics.
Now in the case of QM, and QFT, we are talking about quantum fields. Particles, like the photons, that make up that wave (that we call classical EM wave) are excitation of the QFT fields. These fields exist everywhere in the universe.
The way photons propagate is how we describe how these excitation of the QFT fields propagate in vacuum.
The QFT fields, and their excitation, the photons, are mathematical descriptions, and are the best way to describe them at the quantum level. 
The two level, the classical level and the QM level come together perfectly, the classical emerges from the quantum mechanical.
Maxwell's equations were differential equations and gave solution to wave equation. It was thought that the E field generates a M field and vica versa, but even at that time, they were explaining it with some aether, as medium.
The waves are in phase with each other, so it is not casual. The cause is the source and once the EM wave leaves the source, the phases of the E and M waves are correlated and do not change.
After the Michelson Morley experiment it was experimentally tested that EM waves do not need a medium to propagate.
You are asking why EM waves do not require medium, and the others do. There is no easy intuitive way to think about EM waves propagating in a medium. Their propagation is described by a mathematical theory.
If you would really like to classically think of the EM wave and how it propagates without the medium, you could think of the QFT fields as some kind of media, because the classical EM wave emerges from the QM photon particles, which are excitation of those QFT fields.
The difference is, that the original aether was not Lorentz invariant, but the QFT fields, vacua, are Lorentz invariant.
