It's all great fun, they hop around between alternate realities trying to fix things that got messed up. Psylocke (from the core universe) shows up in the very last couple of plot arcs, and she reads like total fan fiction. She's invisible to the the sensors of the interdimensional hub that lets the Exiles be Exiles, she's unique among every other Elizabeth Braddock in the multiverse. She's a scary ninja lady that enjoys going up against the likes of Sabertooth, she has telekinesis, but she never really uses it, except to create telekinetic katanas. Oh, except she can telekinetically alter her molecules to make her self invisible?
Sometime after that, she is nearly killed, and abducted. For further reasons, she's taken to another dimension where they do something to her. Every time I see this referenced in the comics, there's a slightly different take on it. The end result is that she now appears to be Asian, and has sweet ninja skillz! I have heard it said that her body was simply twisted, and then implanted with skills, I have also heard that her body used to belong to an assassin of the Hand, or that the hand assassin and she were actually merged together. After this rebirth, she stops using her powers like a traditional telepath, although I don't believe they've actually changed, at least not yet. Instead of just reading people's minds, putting them to sleep, or any of the other typical Xavier stuff, she creates a "psychic knife" that projects out of the end of her hand, and "stabs" people with it, which inflicts some kind of psychic assault on them.
I've read an article talking about the racial insensitivity of having a British character becoming suddenly Asian. I'm not sure about any of that, it just sounds stupid. At this point, we've got a character that high school Bryce would think is really awesome. "She was a hot British chick with purple hair, but now she's a hot Asian chick with purple hair, but she speaks with a British accent, she can totally read minds, but instead she, like, makes a knife with her psychic powers, and then stabs her enemies with it and makes them relive all of their worst memories! And she's a ninja!"
So, that's most of the stuff that I know off the top of my head. After another vague amount of time, Psylocke and Jean Grey trade powers, because that's a thing mutants can do (it really isn't). I do remember reading a comic where Jean Grey was stabbing people with a psychic knife, this was also the era where she hooked up with Wolverine. Regardless, Psylocke now has telekinesis as well as telepathy, maybe? Then she shows up in Exiles.
I have read books that feature Psylocke that use her very well, a number of the recent X-Force books for instance, but the way she's used in Exiles just makes me think the writer wants to be her AND marry her.