Humanity can only deduce their presence by unusual radiation spectra and astronomical bodies cauterized by bombardment.
Avoid them by any cost.
Consequently, they are thousands of years ahead of humans technologically.
Avoid them by any cost.
In both cases best strategy is getting know both possible targets, avoid confrontation, buildup human capacities.
Very good if both of those situations take place simultaneously, so those for would like immediate war can test them self against Zaux in limited engagements, specially if for some reason Zaux do not consider that thread as some kind of part of external force. But it have be done very carefully in a way which prevents Zaux consolidation.
###There is a problem with Zaux
As side note, description of Zaux I find it inconsistent
The Zaux have achieved a relatively stable position in this environment, even if they are constantly at war.
The Zaux have limited resources they can divert to deal with them.
Consequently, they are thousands of years ahead of humans technologically.
humanity that has just recently achieved FTL ability.
or that the Zaux are too engaged with more advanced enemies
But they certainly may be a problem in the future specially because of that
Zaux do not realize that humans are an extraterrestrial race
They rely on biological machinery for technology, and are capable of interstellar travel
So a space faring civilization, with blood lust and which is not capable to distinguish between different kinds of treats, with advanced technologies, which finds star system as limited resources, which can utilize war energy and matter waste more efficient then humans do - this may be a problem.
First anomaly
try different probes, which you may think of. Choose one type and send it once a year as example. After thousand years stop sending them, surprise them, let see are they smart and curious or not.