The phrase of none effect is an archaic version of:
of no effect
Nowadays we see an alternation between the so-called determiner no and the pronoun none, such that when there is a following noun we use no, and when there isn't a following noun we use none. In response to Can I have one of your apples, therefore, we might observe either of the following:
- I have no apples.
- I have none.
However, the modern determiner no is derived from older determiner (not pronoun) none. In later English, when used as a determiner, none was used before vowels and h, and no was used before consonants.
This of course mirrors present-day usage of the determiners a and an, where a occurs before consonant sounds and an before vowels:
At around the time of the King James bible, 1611, the use of none as a pre-vowel determiner (as opposed to as a pronoun) had nearly entirely died out. One exception to this was the phrase of none effect, which we see in the Original Poster's example.
This usage has now also disappeared although it survived well into the nineteenth century. We do have one last vestige of it in modern English, though. It still survives in the phrase:
none other than ...
To be entirely in keeping with modern usage this should really be:
no other than ...
In their question the Original Poster asks what role the phrase of none effect plays. The verb phrase in question is equivalent to:
... making the word of God of no effect.
The main verb here is making. It has two complements: the noun phrase the word of God, which is a direct object; and the prepositional phrase of none effect, which functions as a predicative complement ( - object complement). It is so-called because it describes an attribute of the direct object. This is as the Original Poster suspected. Syntactically, the phrase mirrors the structure of:
made the headmistress out of sorts.
**Readers who are able to log-in to the Oxford English Dictionary may be interested in the following: Determiner None OED