An opponent attacked my square and I won, so he retreated the units to the square they came from and were thus routed. Now what would happen if I attacked his square with the routed units on the same turn? Is it like having a zero army? so he can call for support (the square was well supported) or is it like having no army and so it can't be supported and I could just sweep in (and kill his routed units)?

The directions (though clear about nearly every other scenario) don't address this one exactly. They do say that if you attack a square that contains a normal soldier and routed soldiers than only the live soldier counts in defense, but it doesn't specify what happens if you attack a square with only routed soldiers--that could be supported.

After thinking about it, I think its most appropriate to make it an occupied square with a 0 valued army (so the attacked party can call for support and use cards), but I could also make an argument that its like attacking a square with just a power token. Is there an official rule??

ahhh, apparently this was answered in the FAQ (yes it does start a combat with a 0 valued army)...

...and can garner support from those units with a Support Order token...

It is really a normal combat in every respect, with two differences, (1st) the combat strength of all routed units is 0. Example: if you retreated 2 (now routed) units back to a space where you attacked from, where you had had 1 remaining FM (footman - let's say in this example that you brought only 2 of your 3 units from the attacking space to the embattled area, then, your non-routed FM would have a combat strength of 1, and the other 2 units would each have a combat strength of 0.

After calculating initial combat strength, you would then call for support (your own, or other players), recalculate combat strength, and then each player would select and then reveal a House Card, resolved just like a normal combat.

One other difference (2nd): routed units cannot retreat, if you lose, the routed units are all destroyed. I do not believe that routed units may be counted towards satisfying "Swords" combat casualties, so you could lose the non-routed FM as well, but maybe someone else can weigh in on this.