Electromagnetic waves can carry information, but as far as we know they can't process information without some sort of physical object to mediate the interactions between the waves. So the aliens could convert themselves to waves to travel from one place to another, but they would need some physical object that could carry out the computations their brains normally would carry out at either end. It would be like copying their brains from one location to another, they would not be capable of any thought while traveling in wave form.
Even if they could be waves, there is a problem with the idea of them being "all around us". Electromagnetic waves face a number of problems when traveling over great distance that would degrade the quality of the information in the waves. They get smeared both in time and space, they lose energy, they get absorbed, their frequency shifts based on the relative speed of the source and destination as well as the general expansion of the universe. On top of that electromagnetic waves are pretty slow, potentially taking decades or even centuries to travel interplanetary distances. Further, the Earth itself is really good at absorbing electromagnetic waves, so if they were all around us they would be dying as the waves containing them were absorbed by the Earth.
Of course you could throw out the rules of physics as we know them, but then there isn't really any way to answer the question.