[B.T.]

Europe:

If we take a look at the units in Europe, I tend to believe that the symbols of the pacts (Nato and WarPac) would be in widespread use as markings on vehicles. And I can easily imagine, that units, who did not use those before the war, would begin to use them quite frequently: The NATO flag as NATO symbol and the red star as common symbol in units, still operating as part of one of the WarPac armies. Even nations, that did not use them, like Poland as an example, could mark the combat vehicles with the red star.
US units and other NATO units may use the black star of the US forces as common symbol.
A sign that Rainbow mentioned, could be in use, too: The "coalition-V" in white or black on NATO vehicles. But that depends on the background – in my Twilight-world Desert Storm did happen, therefore this sign would be well-known. Without Desert Storm this kind of marking would not be self-evident!

Some thoughts on uniforms and the "marking" of individuals:

This is one of the more complicated issues, because it is very ambivalent. From all I've ever heard, most soldiers are proud of their own tradition(s). Special uniform items or special badges, scrolls and the like are worn with pride. Especially in a situation like the 3rd WW this will certainly be as true as ever. Soldiers from foreign countries would most likely try to show their own national trades or specialities, even if those individual specials do not mean that much to their new comrades (Think of a former Ranger of the US Army wearing the Ranger scroll, now serving with a Danish unit, or something along these lines!).
On the other hand, most soldiers would have difficulties, if they try to wear proper uniforms. Unit tags of some kind are vital! Therefore I usually describe NPCs with a certain kind of clothing, to let the players think about their actions. Depending on situation and distance, a roll for "Observation" may be requested.
In most cases, soldiers will try to wear their own uniform or at least uniform pieces of allied forces. A Soldier, armed with an M16, wearing British trousers, a (West-) German jacket, and a "Fritz"-style helmet looks like NATO. A soldier, armed with an AK, wearing a rain-drop pattern uniform and a Soviet flak-jacket, looks very much as a WarPac combattant. You get the idea.
In most NATO units, I can imagine, that common symbols would be sewn to the upper arms – the NATO flag, the national flag or even the symbol of a certain NATO subunit – from army group to division, tastes vary (In my campaign, most soldiers of the 5th US Corps and other elements of Northag sport the blue shield with the yellow throwing axe as common symbol.). These symbols could be combined: The red diamond of the 5th Inf.Div. on the left arm, and the Northag-shield on the right.

Civilians in units may wear a distinctive armband. In WW II people working for the Wehrmacht (in civilian clothes or in uniform) had an armband with the inscription: "Im Dienst der Wehrmacht" (= roughly: "In service of the Wehrmacht"). Armbands like these would be common. Maybe a blue amband with the NATO flag, or an armband with the US flag (for civilians in a US unit). Think of people like local translaters or craftsmen, that were pressed into service.

Irregular or local forces:

This is a hard one, because several very different units would fall into this catagory. The forces of Filipowitz, the margrave of Silesia, would use another approach as, for example, the militia of an independant city like Krakow.
In the case of a unit, that does not longer see itself as part of the Pact, the unit might use a (simplified) version of the regional symbol – like the flag of the mediveal duchy of Silesia, or the crest of Krakow. In these cases, I think it would be logical, that these emblems would be worn as symbols on the upper arms of tunics or jackets. Maybe there could be a small variant, which would be worn on garrison caps and similar soft covers.
In the case of the militia of a small town, I think that in Poland at least, an easy recognizable item, like a white and red armband, would be in use. Maybe uniform items of the prewar police could be used, if the militiamen are on duty. Something like wearing a police cap and the armband, while the man is manning a post as guard in the city. I think we discussed this issue a while ago: What is called "ORMO" in the modules of GDW, was not necessarily ORMO in Poland. Different organisations were summarized under this term. Where remnants of these other organisations exist, these might still use the prewar emblems.

Some thoughts from my point of view. I do not have enough insights to try something on the MilGov/CivGov debate, so I'll skip that one.