This series actually go in pair with each episodes of the main series. Which I find nice. Unlike what you could find with picture dramas from Code Geas for example that requires you to have seen the whole show for it not to spoil you.
I enjoyed it because it is more than just putting characters out of the show in extras where they do stuff. This can actually be both considered canon and develops a bit more the characters on a lighter tone than the main series.
So far I have not often seen such extras and I find it refreshing.
Youjo Shenki isn't really what I'd call a 'parody', but more of a short 'behind-the-scenes' series featuring Tanya and the main battalion members simply sharing conversations and having a laugh.
The animation is very simple, using chibi characters and few frames.
It is not meant to be taken too seriously in comparison to the anime, nor does watching it have much benefit - it is simply a little something extra for anyone who wants it.
I personally felt some of the episodes were a little boring, but some certainly were worth watching for the amusement.
~Should you watch it?~
If you enjoyed the anime and wouldn't mind seeing a bit
more of the characters, like chibis and light humour, by all means give it a go.
I can only recommend watching episodes 1,2,5,6 at most.
This is, first of all, not really a parody of the main series. It is more of a supplement to the anime, showing some of the battalion while out of combat. Some of the time is spent discussing events in the main series, while the rest is spent on off duty discussions or shenanigans, and these shorts loosely follow the same chronology.
That said, except for a few episodes, this is, in my opinion, not worth watching. After finishing the main show, I went into this wanting a little something extra, and though it is meant to be
humorous and be a little service to the fans, it fell very very short. The "humour" is made to be character-driven but is generally just not present, and the dialogue (which is usually the totality of little chibi shorts such as this one) is dull and poorly written and will probably want to make you skip through it. Oh well.
It's the product (I suspect) of a few animators with too much time on their hands asking some of the voice actors to come do some stupid shenanigans with them. That said, it can actually be amusing. As far as parodies go, this one isn't bad, though I'd definitely recommend watching the actually show first, or alongside, since it make direct reference to it on a regular basis.
It follows the off-battle exploits of Tanya and her squad, from rotten potatoes to chocolate. It's really good stuff for when you're either a fanboy,
or high, or both. That's not meant as an insult by the way - this isn't on the level of the actual show because it isn't meant to be.
Please enjoy, and if you're not into chibi then don't watch it and get mad. Please.