Sure, you can juice with a blender, as long as (a) the blender is of reasonably good quality and (b) you're not expecting the same kind of yield or quality you'd get with a juicer (electric or manual). You'll also need a very fine strainer, or cheesecloth if you're like me and hate any amount of pulp.
You'll have to peel them first, and try to remove the pips as well (clementines shouldn't have very many, and might even be totally seedless). The pith is less of an issue - some people remove it, some people don't, it's a matter of personal preference. Once the oranges have been "cleaned", start blending them on the lowest speed and gradually bring it up to high. Oranges should have enough juice to blend on their own, but regardless of what fruit you use, be prepared to add water if the blender doesn't seem to be doing much.
Once you've got a fairly consistent purée, pass it through the strainer and mash the pulp against it with the back of a spoon or the bottom of a glass jar. There's your juice. You can throw some pulp (purée) back in if you like that texture.
Fruit purée from a blender doesn't really have the best flavour - it tends to turn out somewhat bitter - so you'll probably want to add a small amount of sugar and/or citric acid to compensate.
Some quick research indicates there are enzymes in freshly-squeezed juice that will degrade it fairly rapidly, and that they can be deactivated by heat. Of course, that also changes the flavor (especially since you're not going to be able to quickly heat and cool it, as it apparently only takes 30 seconds, but any method doable in a home kitchen will keep it hot much longer than that). So heat-deactivation is out.
Even commercially-produced (that is, both pasteurized and enzyme-deactivated) juice is only supposed to keep 6 days in the fridge, so that's out.
Your best bet, then, is to freeze it. According to the University of California's Division of Agriculture and Natural Resources Publication 8199, you can freeze in clean glass jars or rigid plastic freeze containers. They also note that navel oranges (and their juice) do not freeze well—they will become bitter.
Well, either that, or store the fruit instead, and only juice it as needed.
Best Answer
This isn't exactly scientific but..
Taste. Specifically looking for the taste difference between pasteurized and un-pasteurized juice. Pasteurized orange juice has a distinct tart taste that just isn't there with fresh juice.
I guess it depends on your exact meaning of "fresh", but if it hasn't been pasteurized then it will have a shelf-life of only a few days.
The legal specifics of the terms will vary from country to country, so if you have one in mind then you might have to mention that. Although as you hinted at, the legally defined terms are often side-stepped and might not be much use.