Strictly speaking, it is not IMPOSSIBLE to earn NW miles going to Australia. However, you would have to go either through ICN on KE, or through Europe on KLM/AF. Either of those options is likely to be completely impractical from a financial standpoint, and is definitely impractical from a time & convenience standpoint. So, I'll grant you that it's not the best program if you're going to be flying back and forth US-Australia regularly.
The 2 airlines that have nonstops from LAX-SYD are United (Star Alliance) and Qantas (Oneworld). United also has service SFO-SYD and Air Canada (another Star Alliance carrier) has nonstop HNL-SYD. So strictly from the standpoint of Australia access, you're probably best off going with United since you have 3 nonstop flights US-Australia per day in that alliance vs. one in Oneworld and none in Skyteam.
The Europe flights are pretty much a wash; any major US airline can fly you there and you will earn full EQMs in their program. The only catch might be if you flew BA across the Atlantic, which does not earn miles in AA. Again, it seems a slight nod to Star Alliance over Oneworld.
The flight to YUL - again, anyone can do it, but Star Alliance will have the only nonstop service LAX-YUL (Air Canada).
As far as going back and forth to NJ - you don't say where in NJ, but if you don't mind flying into a New York area airport you might be able to experience United's P.S. out of LAX. AA doesn't have anything comparable.
As far as getting upgraded on the transcons...you probably actually have a better shot of that on United or AA than you would on a Skyteam airline anyway. Skyteam airlines all give complimentary upgrades to their elites (and, in the case of CO and NW, reciprocally to one another's elites) so unless you are a Plat, it may be difficult to get upgrades on heavily traveled routes with lots of elites (such as transcons). AA and UA both make you use some form of coupon to get upgrades, but you earn the coupons by flying and/or can purchase them. I don't fly either airline transcon enough to know what your chances of finding yourself shut out of upgrades as a low-level elite would be; perhaps others can speak to that better. However, I would add that on UA you can get into E+ even as a low-level elite, which, while not first class, is better than nothing (i.e. better than a regular coach seat on NW/CO/DL/AA/WN/whoever).
For all of the above reasons, I would probably go with United based on your upcoming flying patterns, but would advise you to get more than one opinion from others more knowledgable than me, too!