She's probably all of those things -- and she brings a bit of each to Welcome to Me, a purposefully weird comedy in which Wiig plays Alice Klieg, a woman suffering from borderline personality disorder.
Alice's life changes when she wins the California lottery and decides to use her new-found fortune to finance her own talk show.
Obviously no one in his or her right mind would put someone like Alice on TV -- except for a financially strapped production company that's wallowing in failed infomercials.
As a compulsive fan of Oprah Winfrey, Alice believes that she can become a talk show host, but her idea of a talk show involves sharing weird recipes (a meatloaf cake), near-hysterical reenactments of childhood traumas and a series of programs devoted to neutering dogs.
I'd be lying if I told you I knew exactly what to make of Welcome to Me, which was directed by Shira Piven from a screenplay by Eliot Laurence.
The movie made me laugh; it made me queasy and, by the end, I concluded that it couldn't quite sustain its crazy premise.
Still, Wiig doesn't flinch from the challenge of carrying the movie, even though she receives support from Wes Bentley and James Marsden, as the owners of the infomercial business, as well as from Joan Cusack, as the show's director. Linda Cardellini plays Alice's best friend, and Tim Robbins appears as Alice's therapist, a role that's handled with enough seriousness to keep the movie off-balance.
But then everything about Welcome to Me is a bit off-balance, and I imagine that audiences will include those who laugh, those who squirm and perhaps even a few who walk out.
Wiig has had big hits (Bridesmaids), voiced animated characters (How to Train Your Dragon) and veered away from the mainstream (The Skeleton Twins).
Welcome to Me again takes Wiig off the beaten track with a comedy about a mentally ill character who finds a temporary home on television. Draw your own conclusions.
It probably would be wrong to categorize Welcome to Me as any kind of media satire: Like Wiig, it exists in its own category-resistant world -- and probably is better off for it.