A colleague writes:
"It makes sense [to translate "oder" as "or" here], since, I believe, the stickers are for each city, and having a sticker from one city doesn't necessarily mean you can enter another city...or does it?"
In fact, Germany has green, yellow, and red stickers for cars now, and those stickers apply across the nation. Wherever I get my green sticker, it is green throughout Germany – yet another example of how the Germans use "oder" incorrectly, thereby misleading readers.
Yes, you can use the same green sticker to get into downtown Munich, Stuttgart, Berlin, and (!) Heidelberg.