is there any theory or observational evidence that our universe is electrically neutral or not? It seems our universe is neutral in large scale.

There is CP violationwiki problem about matter and dark matter. 
Similarly is there any theory about whether our universe is electrically neutral?

Cosmic rays are not neutral. However the atomic nucleus and electrons are just separated. There should be no charge excess in total.

What is the largest scale that is severely non-neutral?
By observation, gravity dominates the universe on large scales.  If there were a significant disparity in positive and negative charges then we would expect electromagnetism&mdash;which is approximately $10^{39}$ times more powerful than gravity&mdash;to dominate.  So by this observation we can conclude that the universe is approximiately electrically neutral.  Exactly why this should be so is not well-understood, and ultimately ties into the matter-antimatter problem, aka the baryon asymmetry.

Protons and electrons are produced through distinct processes.  That we have many protons is not particularly remarkable, as this would come about by conservation of baryon numbers as other particles decayed.  Why we have any electrons at all is a fair bit more mysterious.

In the early universe, we understand the energy was well above the electron-positron pair production threshold, and so the early universe had large amounts of both electrons and positrons.  When the universe cooled below this threshold, the production would have stopped and we would expect the electrons and positrons to then collide and annihilate each other, leaving essentially none of either.  But we obviously see large amounts of electrons: approximately as many electrons as protons by the aforementioned observational evidence.  And we also do not see large amounts of antimatter&mdash;positrons in particular.  If there were large amounts of positrons out there, we would expect to see tell-tale signatures in space as they annihilate with regular matter (or in any weak force interactions, such as would be evident in supernovae), and we have no such observations.

So somehow the early universe must have produced significantly more electrons than positrons.  In other words, we have strong observational evidence that there must be an asymmetry in physics between matter and antimatter production.  There are ways to work this into the theory, but the Standard Model by default does not support it, and experts have not really settled on any one particular modification.