what is a soul made of and how come the mechs have several?
The souls are not literal souls, but instead concentrated magical energy that once belonged to a member of the Ancient Dragon Tribes. It's essentially part of their innate magic, and they can use them to give certain things power, or just draw energy from them into themselves. The Terrarians have the ability to use them as a power source as well, but can't draw energy directly from them and harness it, and usually waste a large portion of the power within the souls because they aren't very efficient at crafting with them.
Souls of Flight are used by the Feathered Tribe (Wyverns) to keep a shield around them at all times so they can breathe even outside of the atmosphere and can't be sickened by intersteller radiation, and they also use them to fly.
Souls of Light and Night are employed by the Gilled Tribe (Pigrons) to imbue the creatures in their respective biomes in an attempt to foil the ones who they believe are a danger to the Six. These ones are highly unstable due to the feral minds of their owners (if your mind isn't focused, neither is your magic), so they often disappear outright once their owners are destroyed.
Souls of Fright are the rarest ones, because they belonged to the now extinct Furred Tribe. We unfortunately didn't gain the ability to study what they were capable of before the Furred Tribe went extinct, but they seem to have a great deal of potential. If only anyone could tap into it... but unfortunately not even the Terrarians seem to be able to come up with anything particularly useful with them.
Souls of Might were used by the Scaled Tribe before they lost most of their power and became the Lihzahrds. They are used to create weapon that are both straightforward and have the potential to be overwhelmingly powerful in the right hands. These are almost as rare as Souls of Fright, unfortunately, so only the Destroyer got any significant usage of them.
Souls of Sight are used by the Shelled Tribe (Derplings). We can use them to see in any wavelength of the electromagnetic spectrum, and occasionally predict a few seconds into the future (we never really get anything useful from it though, and we can't do it on command.) They have the ability to focus light in a myriad of ways, including outwards as powerful projectiles, or inwards in order to see great distances and filter extreme darkness/light.