Strike Witches/WMG

The Neuroi are The Heartless / Enemy Without of Mankind
World War II, the war to end all wars. The Holocaust, all those terrible things were averted in this verse because all the death, all the inhumanity to man coalesced outside the human heart and started killing people instead of people doing it.
 * Was the destruction of most of the world worth avoiding Hitler's Time Travel Exemption Act or Godwin's Law of Time Travel? Maybe.

Erika is a tactical genius who is just too lazy to use her mind
As evidenced by episode 4 of the second season, and her sister's personality from the novels. She probably passed by the briefing room and caught a glimpse of how fast the Neuroi was. She knew Shirely would be assigned to attack the core-section but would be unable to catch-up. She gave Trude the transmitter so she would use the Jet Striker to save Shirely. Additionally, she knew this would mend their relationship by the end. I think the french fries also probably factored into her plan somewhere along the way. -- Andaria

Mina
Since her magic makes her the C-n-C for the squad. She knew all along...

Sora no Woto is the distant future of Strike Witches
Note: I haven't formally watched the former show. Ok so after the Neuroi are defeated/reasoned with, the army still has to put all these young girls somewhere, thus leads to the new female squadrons. The level of technology is on par, and both shows imply a Japanese or global diaspora. -- Andaria
 * No one in the Sora no Woto setting is capable of using magic, so it doesn't seem like it would be the same world. Although one could argue that the Magitech used in Strike Witches was adapted to make the spider Tanks and other black boxes of Sora no Woto, and that there is no depiction of magic simply because no magic users actually appear. And I just killed my own argument, but oh well. --PacSol

Strike Witches takes place in the year 3954 a.C (after Christ) A.K.A. 1939 a.I (after Instrumentality)
I get this idea when i read another WMG in the Code Geass page (i actually see this one as a prequel of the Code Geass one) that is also about Strike Witches.

I think that after the two types of Seeds of Life where spread around the galaxy, the First Ancestral Race created a thirth type based on Adam and spred it too or maybe they just spread a prototype of the Adam-class seed along the other two. Those were the Neurois and after centuries of evolving they got their own reasons of take over other planets. After End of Eva maybe a part human population that return to their human form decide to start over. In 1939 after the restart of humanity, the Neurois arrive to earth and begin to attack and that is when Strike Witches begin.

Here are the similarities between Angels and Neurois that make thing they are related:
 * Both are aliens
 * Both have regenerative abilities
 * The only way to destroy/kill them is destroying their core.
 * Both can take a humanoid form: Kaworu in the Angels side and in the Neurois side the one who looks like a Witch with an Striker Unit.
 * The weapons of the humans side have origins related with the enemy: Eva Series an the Warlock's energy source. This leads us to...
 * Both "infected" the human weapons that are related to them: Eva-03 in the Angels side and the Warlock in the Neurois side.

At least this is my idea and I think it could make some sence. Also the magic could be a side effect of Instrumentality.

The Neuroi are split into two fractions
On one hand we have the warmonger, who want it "Us or them", represented by the maschine-like Neuroi and on the other we have the peace willing Neuroi, represented by the humanoid Neuroi.

That would explain why the humanoid Neuroi in the beginning of Season 2 was destroyed: the warmongers couldn't allow them to start neogations.

Dr. Miyafuji lives
I see two possiblities: Fuso/Britannia is hiding him to let/make him work without interruptions. He still gets time to work on Strikers for his daughter, probably based on reports he gets over military channels.

The other is that he went into hiding so that he doesn't have to develop war machinery. He still wants his daughter to be safe and develops new Striker for her. Where his information come in this case is another question.
 * Not only is he alive, but he's somehow connected to the Neuroi, hence his ability to send plans for new, more advanced equipment just long enough before things go badly for a solution to be available.

The underwear bug was Not So Harmless
All we know of the bug (from S2 E7) is it drains energy and likes witch butts. Now, there's nothing special about that area — except when the witch is using magical energy. If it really could suck the power out of an active witch, the underwear targeting was not random but a logical (if underinformed) covert attack. Whether it would let the Neuroi use witch magic or simply cripple or kill the witch is speculation upon speculation.
 * Since the 'drone' part increased in size when the core drained energy, it was likely targeting high-energy sources...power cables and the witches...in order to increase its own strength. Even if it merely inconvenienced the witch it was draining, it would make the attack-form stronger, while at the same time, being in a form that, while fragile, was far too small and agile to attack directly. It was just bad luck that Minna has Buns Of Steel.

This map of the Strike Witches world is..

 * What happened to Amer.. I mean Liberion.
 * Hamfisted symbolism by the look of it, just look at the shape it pretty obviously forms a crude five pointed star.

The Neuroi are a Nazi experiment that got out of control

 * The Neuroi were an experiment for war by the Nazis in Karlsland after they came to power. Then the Neuroi got loose and started destroying all of humanity, thus being able to combine the nations on both sides of WWII to fight the Neuroi.
 * Jossed, since thankfully the Nazis never took over power in Karlsland.

The Neuroi are Transformers

 * They can assimilate with technology and transform. The Decepticons are the Neuroi fighting the witches, the humanoid Neuroi that tried to communicate with the humans are Autobot envoys, who were destroyed by the Decepticons. The Transformers also have appeared in human history.

The Neuroi are Cousins of the Dalek

 * Well; a Doctor Who theme hasn't been suggested yet. They are apparently part machine and seem to like killing humans for absolutely no reason other than they exist.

The reason, why Anna Ferrara is that good at broom riding
She's living alone there and get's lonely, so she uses the broom to relieve tension (look at how Miyafuji, Yoshika and Perrine reacted the first time).