Transit Through City of Origin?
 

It seems unclear to me how "point" of origin is defined on the OWE fares. Are co-terminals part of the same "point"?

Basically, is this allowed:
JFK-SYD-......-LHR-EWR-ORD-LGA?

I'm not technically returning to my airport of origin (JFK) by transiting through EWR to ORD (I would like to do this to return home for a few days mid-trip), but if the OWE rules consider JFK/EWR/LGA the same point, clearly this violates the rule about returning to the city of origin.
Does it matter if EWR is a transit with or without stopover?

Thanks!

It would only "not matter" if the LHR-EWR-ORD flight was one flight number. If not then it doesn't matter if you are in EWR for less than or more than 24 hours.

As to the other question, I don't know, but my guess would be terminals in the same city (JFK/LGA/EWR) are considered the same "point of origin" with respect to the particular rule you are asking about. But more those knowledgeable will correct me - or someone who has actually done this.

Coterminals are considered to be the same city, and your trip ends when you reach a coterminal (EWR in your example). This is a very firm rule. There is a list of coterminals published on each of the airline web sites (sorry, don't have the URLs, but they have all the obvious ones covered and also include some more distant coterminal airports -- this rule is really bulletproof).
Edited to add the best you can do is return to a nearby city like Boston or I think White Plains and Newburgh are not coterminal in NYC (not 100% sure about the last 2, but getting to them would waste a segment). Maybe MCO is a good stopover city for NYC (presumably lots of flights and cheap fares).

HPN and SWF pop up as coterminals every now and then, but are usually pretty safe. At times I have found airlines treating EWR differently than JFK/LGA, but that tends to be rare.

BOS isn't too far, and you could always catch the super-cheap Chinatown bus if you are on a strict budget.

PHL would be another fairly close option.