No - this doesn't work in the Asia/SWP bit - you can only enter each continent once, and you are entering Asia twice. There is an exception if one entry into Asia is a transit without stopover between SWP and Europe (and perhaps, depending on who is interpreting the rules, a transit without stopover between SWP and NA).
It also doesn't work in NA because you cannot backtrack to the mainland from HNL.
http://www.fewmiles.net/oneworld has the full fare rules, but you could get the same destinations (& some others) with this routing:
GIB-LHR-DXB-LHR-HKG-MNL-HKG-BKK-SIN-MEL-AKL-CHC-WLG-SYD-HNL-DFW-ORD-SJU-IAD-LAX-LHR-GIB
This is BA, CX, QF. You have one more segment in NA if you want.
(I assume when you said OY you meant AY, Finnair, which is possible BKK-SIN, but I would take CX)
To maximise mileage, you can get longer segments in Australia (go to Perth or somewhere), and in NA by going to Anchorage.
The only restriction on stopovers is that of your four arrivals in Europe (LHR, DXB, LHR, LHR) at least two must be transits (i.e. no more than 23 hrs 59 mins before you take the next flight). In the other continents the only restrictions are on numbers of segments.
[This message has been edited by christep (edited 09-20-2002).]