The latest episode of the sci-fi franchise won the top honour of outstanding visual effects in a photoreal feature.
It also scooped awards for outstanding models, created environments and virtual cinematography.
The Good Dinosaur won the most awards in the animated feature competition.
The Revenant, starring Leonardo DiCaprio, tells of a 19th Century fur trapper on the American frontier who wages a gruelling battle for survival after he is savagely mauled by a bear and left for dead by his callow fellow hunters.
The bear attack scene won two awards, for outstanding animated performance and best compositing, with the third award in the best supporting visual effects category.
Mad Max: Fury Road won the effects simulation award.
It is nominated for the visual effects Oscar, alongside The Revenant, Star Wars, The Martian and Ex Machina.
The Good Dinosaur's awards were for outstanding visual effects in an animated feature, outstanding created environment and outstanding effects simulations.
Game of Thrones won four awards in the television categories.
Alien and The Martian director Sir Ridley Scott was presented with the lifetime achievement award at the ceremony, with conceptual artist Syd Mead winning the visionary award.
Star Wars: The Force Awakens has taken home the most trophies at the Visual Effects Society Awards in Los Angeles, with The Revenant collecting three.