Who or what are the legions and orders?

[TemplarGFX]

Weapons have attributes like extra attack vs Legion of Immortality, Legion of Death and the Order of Truth

What in the hells are they? How do I know what enemies belong to what faction?

[Puzmen26]

You can get acquainted with their unique looks after unlocking the Lab and investigating them without getting shot. The mission location tooltips on the map also mention the enemy group to be expected when you go there. You can also scan them mid-fight and identify them by weakness:
-Toxic & Crushing > Legion of Immortality
-Electric & Burst > Order of Truth
-Ice & Piercing > Legion of Darkness