Answer by taking a quote from the following article:

Hoodoo Gurus (referred to as the Gurus by fans) are an Australian rock band, formed in Sydney in 1981, by the mainstay Dave Faulkner (songwriter, lead singer and guitarist) and later joined by Richard Grossman (bass), Mark Kingsmill (drums), and Brad Shepherd (guitar, vocals, harmonica). Their popularity peaked in the mid to late 1980s with albums Mars Needs Guitars!, Blow Your Cool! and Magnum Cum Louder.

Three Hoodoo Gurus founders were from Perth protopunk and punk bands: Dave Faulkner (guitars) and James Baker (drums) of The Victims; while Baker had been with Roddy Radalj (aka Roddy Ray'Da) (guitars) in The Scientists. The fourth founding member, Kimble Rendall (guitars) was formerly in Sydney punk rockers XL Capris. The three guitarists Faulkner, Rendall and Radalj met at an end-of-1980 New Year's Eve party and were joined by Baker to form Le Hoodoo Gurus.  Le Hoodoo Gurus unorthodox line-up of three guitars and no bass player, fused pop melodies, punk guitars and an American trash culture ethic. This was captured on their first single, "Leilani" released in October 1982, on Phantom Records. This told the story of a maiden sacrificed to the gods and an erupting volcano while her true love looked on helplessly. They dropped the 'Le', to become Hoodoo Gurus, not long after the single's release. As the Hoodoo Gurus, they gave their first ever performance on a segment of the kids' TV program Simon Townsend's Wonder World; this was followed by a performance alongside a man and his singing dog, on The Don Lane Show.  Rendall left in 1982 before the release of "Leilani", and went on to become an award-winning music video and film director. Rendall was Second Unit Director on the latter two Matrix films, The Matrix Reloaded and The Matrix Revolutions, as well as I, Robot. Rendall also directed the slasher film, Cut in 2000. Rendall was effectively replaced by Clyde Bramley (bass guitar, backing vocals) from Sydney bands The Hitmen and Super K.  Radalj was not happy with Rendall's leaving or Faulkner's greater influence and left the Gurus. He was replaced by ex-Fun Things guitarist Brad Shepherd, who had been Bramley's flatmate. Bramley and Shepherd had both been in The Hitmen and Super K. Faulkner wrote "I Want You Back" in response to Radalj's public dissatisfaction with the Gurus. Radalj went on to perform with a number of other acts, including The Johnnys, Love Rodeo, The Dubrovniks and Roddy Ray'Da & the Surfin' Caesars. As Roddy Ray'Da, he released Lost, Lonely and Vicious in 1990, Orgazmatazz a year later and Mouthful of Chicken in 1993.

When was the band formed?
The three guitarists Faulkner, Rendall and Radalj met at an end-of-1980 New Year's Eve party and were joined by Baker to form Le Hoodoo Gurus.