Dr. Hilarius is Oedipa's psychotherapist. He tries to recruit her for an experiment on the effects of LSD and other hallucinogenic drugs, which she refuses (good call, Oedipa). We also learn that Hilarius has some very unusual therapeutic methods, including making weird faces at his patients in the hopes of curing them.
Late in the novel, when Oedipa worries that she is losing her mind, she seeks out Hilarius for help. It turns out that Hilarius has already gone crazy. He takes her hostage with a German rifle, and reveals that he was a Nazi at the Buchenwald concentration camp in charge of projects dealing with experimentally induced insanity, particularly those related to faces. Now he is afraid that he will be taken back to Israel to stand trial.
Weirdly, Hilarius thinks he has some claim to sympathy. He tells Oedipa that he has been working as a Freudian therapist ever since the war as penance (since Freud was a Jew). As he says, "If I'd been a real Nazi I'd have chosen Jung, nicht war?" (6.177).
Whatever you say, Hilarius.
The police break in and take Hilarius, but the damage isn't over. When Oedipa goes back to see Mucho, she learns that Hilarius was giving him LSD, and that Mucho has also lost his mind.
You'd think that because Hilarius is a therapist he'd be a fairly stable character. Instead, he's the craziest character in the book, who seems to infect everyone he touches with madness. Pynchon uses the Nazi doctor to satirize psychotherapy, clearly suggesting that therapists are just as messed up as everyone else (if not way more so).