Not sure about the different sounds causing different effects, in terms of doing meditation, as the purpose of the mantra is to take us away from the thoughts in the mind.
Yes, with TM, there are these 16 mantra that relate to deities in vedic teachings, but the fact that they are given to the student based on the age they are at the time they learn meditation, clearly indicates that the different sounds are not actually important for TM. When Maharishi Mahesh Yogi brought TM to the West in the 60's, he himself said that any word could be used as a mantra. The interesting thing with TM is that when the student is given their mantra, they are told it is personal to them, and they are not (as far as I'm aware) told that their sound is the name of a deity from Hindu/Vedic teachings or that the ceremonial induction into TM is based around praising the deities and gods of that philosophy.
Of course, different sounds do have different effects if we use the sounds for such purposes and we are focused on them, as we have with Sound Healing techniques.
The origins of the universe are thought to be linked to sounds.
This is true. If we look at what sounds are, they are vibrations of particles and particles are, according to Einsteins equation, energy. In fact the whole of the universe according to that equation, is energy. Science talks of the "Big Bang", Religion talks of "In the beginning was the word", the word being a sound and, logically, we can say that any movement, vibration of particles can produce sound. So, from the moment the universe was created (assuming you believe in creationism), there was vibration and thus sound, and these different vibrations, these different sounds, are what create the different matter in the universe.