First off, i'm just going to say this about 2 countries:
North Korea : cannot even feed its own army. Yes they have a much bigger army than us, but unless they had a modern and capable navy (which they dont) they have no way to get them to our shores. We would achieve 1000 to 1 kill death ratio against them in the sea.
Indonesia : Similar problem to North Korea, too many tech generations behind us. Not enough GDP to build enough new stuff to compete with us. They are much closer though so perhaps they could build a bazzillion small cheap boats and send them all over thus negating our technology somewhat. (i dont know how many anti-ship missiles/torpodoes we have, but i'm sure it wouldn't be in the tens of thousands)
Strategy:
I dont really know, but I would attack from the bottom where the Jindalee over the horizon radar doesn't cover. Of course this will require a decent navy to sail all the way around there.
Nuclear weapons: They exist, so you cant just "rule them out". Russia for example could nuke all our capitals thus significantly reducing our will to fight. The resources they would be invading for are not in the capital cities anyway.
My original comment that Smokey was perhaps referring to was me saying Australia could be invaded in the future so the invaders could secure resources. This does not have to be done by any solo country, and of course, we probably would not have to defend ourselves solo. Assuming the US is defending us vigorously we certainly would not be able to be invaded by anyone, or any combination of countries except perhaps the ENTIRE rest of the world.
Assuming its a perfect 1 on 1, and noone has allies, any country with significantly more GDP & Population than us would be able to invade us after some military spending and buildup, regardless of what military equipment they have at the moment.
http://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nominal)
Germany, France, UK, China etc all have excess of double our GDP, and would be able to invade us if they put in an effort and really tried (of course they may have to build up their navies in secret for a couple of years before they can give it a shot)
Exactly as everything is now (but assuming no allies), I think there are few countries that could invade us, but I dont think the US is the ONLY one.
Russia and China (especially once China gets its aircraft carrier) could, IMO, almost certainly invade us, if not before some nuking, after.
UK and France possibly.
*edit*
I should just state though, I think we have a great military, that is technologically advanced, well trained, disciplined etc. Yes there are some silly things that go on, but that will happen in any large government organization. I dont think anything needs to be done to "improve" our military. I dont think we should increase our military spending.
But if your going to put 30,000 soldiers against over 2 million (china), they dont have to be good or excellent, they have to be f'n unbelievable.
That sided with the fact that the Australians are backed up by 20,000,000 people and an industrial machine that consists of a rotary washing line and lawnmower factory, and the Chinese are backed up by billions of people and a huge industrial machine, I just dont see how they would be unable to invade us.
*edit 2*
ooh, i lied, i got curious and looked it up, the hills hoist washing line is actually made in china now. I wonder if we still make the mowers...