From October 1999 to 2013, Palka was in a relationship with actor Jason Ritter. The two met while both were studying at Atlantic Theater Company.
Palka wrote, directed and starred in Good Dick, which competed in the Dramatic Competition at the 2008 Sundance Film Festival. The film also featured Jason Ritter, Martin Starr, Mark Webber, Charles Durning and Tom Arnold. The New York Times said the film "surmounts its indie-movie quirkiness with exceptional acting and a sincere belief in the salvation of its wounded characters.” Palka returned to 2010 Sundance Film Festival as a Juror with the Alfred P. Sloan Foundation.
In 2010, Palka performed in Love, Loss, and What I Wore at The Geffen Playhouse in Los Angeles. In 2012, she was in The Ensemble Theater in Santa Barbara, California, reading of The Good Soldier. She appeared in Martin McDonagh's The Lonesome West at the Actor’s Gang Theatre, Los Angeles, and in Conor McPherson's Dublin Carol at the Ensemble Theatre Company.
Palka wrote, directed and starred in Bitch, based on a true story from Scottish Doctor R.D. Laing of a mother acting like a dog after a psychotic break. The film made its round in film festivals around the world, after its world premiere at 2017 Sundance Film Festival. In 2017, Palka directed the feature film EGG starring Christina Hendricks, Alysia Reiner and Anna Camp and produced by Michele Ganeless.
Palka appeared in Peter Mullan’s Neds, Jeremiah Jones’ Restive, Bryce Dallas Howard’s When You Find Me, Nathan Sutton’s Autumn Wanderer and Sylvia Sether’s King of Norway. In 2014, Palka produced and was the subject of the HBO Lucy Walker documentary The Lions Mouth Opens which was nominated for an Emmy Award and shortlisted for an Academy Award nomination. Palka made a cameo in the HBO series Girls as Jessa’s (Jemima Kirke) sister. As of 2017, Palka appears as Reggie 'Vicky the Viking' Walsh in the Netflix series G.L.O.W .