I don't understand the wording on this feat card. How can a figure have all these preqs at the same time?

Technically, they can't (at least, not without some shennanigans). Which is where the Marvel errata comes in:

Replace the text on the card with: “Prerequisites: Outwit and Perplex Choose a character. Outwit does not need to show in the character’s stat slot in order for the character to use this feat. When the character uses Perplex, it may affect every target friendly character within 10 squares of it that shares a team ability with it. The character must have clear line of fire to each target.”

In other words, Outwit must still be on the dial somewhere, but in order to actually use the Feat, only Perplex must be showing.

Note, too, that character must meet the prerequisits before the game begins. Mystique, for example, could not be a Brilliant Tactician since she only has Perplex on her dial during team construction (even if you were planning on using Oracle on her card to give Mystique Outwit).

Additionally, you can use Brilliant Tactician even when Perplex ISN'T showing on your character's dial, so long as the BT is an agent of Oracle, and you're playing Oracle on her card.

In that case, you can have, say, your Vet Beast take a power action to gain perplex from her, then use the free action of perplex to trigger the Brilliant Tactician feat card. Note that Vet Beast, or whomever you're playing the feat on, still HAS to meet the pre-reqs for the feat BEFORE he gains it from Oracle. Adding her to the team is just a way to ensure you've always got access to the feat so long as your character is alive.

Dude... I hadn't thought of this. Brilliant!

I prefer V Taskmaster (since his Wildcard TA makes BT even more flexible), but that is a very potent strategy.

So the only time you can really use BT, is when the choosen character has perplex showing on its dial.

Correct.

Although I'm really tempted to go for a large point Avengers team which has V Cap, E Shaman, and LE Tony Stark (if I ever get one), and put Brilliant Tactician on all of them.

Which probably isn't the best use of points, especially on Cap, but that one shining moment when I'm triple-perplexing everything in sight would sure be sweet.

The big queation is: how many other figs will there be to perplex when you invest almost 400 points in those three figs alone?

Jarvis, the 4-damage-causin' butler, baby.

That is awesome, I wish I would have thought of that. I can't wait to try it.