'waxing' means growing, getting brighter. It is usually used when talking about the moon. The moon is waxing when it gets a bit bigger every night, and waning when it passes full moon and starts to get smaller.
'eloquent' means good at speaking, and usually means forceful and convincing.
Wax eloquent means, in it's most literal form, 'to become able to speak convincingly', and means by association that you know a lot about the particular subjesct and enjoy talking about it.
'to harvest souls' means to collect peoples souls, which by association means kill them - you have to die to lose your soul.