Banzai (Peter Weller) prepares to test his Jet Car, a modified Ford F-350 pickup truck powered by a jet engine and capable of exceeding the speed of sound. The car is also equipped with a secret device called an "oscillation overthruster", which Banzai and his associates hope will allow it to drive through solid matter. The test is a success: Banzai stuns onlookers by driving the Jet Car directly through a mountain. Emerging on the other side, Banzai finds that an alien organism has attached itself to the undercarriage.
Hearing of Banzai's success, physicist Dr. Emilio Lizardo (John Lithgow) breaks out of the Trenton Home for the Criminally Insane, after being held there for 50 years. A flashback shows Banzai's mentor, Dr. Hikita (Robert Ito), was present at Lizardo's failed overthruster experiment in 1938. Crashing half through the target wall, Lizardo had been briefly trapped in the 8th dimension where his mind was taken over by Lord John Whorfin.
Whorfin is the leader of the Red Lectroids, a race of alien reptiles who wage war against Planet 10. After being defeated by the less-aggressive Black Lectroids, Whorfin and his group were banished into the eighth dimension. Lizardo's failed experiment accidentally released Whorfin and he soon brings many of the Red Lectroids to Earth in an incident that was reported in 1938 by Orson Welles in his radio broadcast The War of the Worlds, only to be forced by the aliens to retract it all as fiction.
The Red Lectroids now pose as employees of the defense contracting company named Yoyodyne Propulsion Systems. They have been working on building a large spacecraft under the guise of a United States Air Force program, the Truncheon bomber. They intend to rescue the remaining 8th dimension exiles and take over Planet 10. They were unable to produce a working overthruster like Banzai's, so Whorfin plans to steal it. Banzai's team, the Hong Kong Cavaliers, finds out about Yoyodyne and hacks into their computer. They discover that everyone there has the first name John, with various last names such as Yaya, Smallberries and BigbootĂŠ. At first they believe it to be a joke, but then they notice all the Yoyodyne employees applied for Social Security cards on November 1, 1938 and all in the same town: Grover's Mill, New Jersey.
In the meantime, a Black Lectroid spacecraft orbiting Earth contacts Banzai, giving him an electric shock that enables him to see through Lectroids' camouflage. (Black Lectroids appear to be Rastafarian Jamaicans, while Red Lectroids appear to be Caucasians.) The ship also sends a "thermo-pod" to Earth, with a holographic message from the Black Lectroids' leader, John Emdall (Rosalind Cash), explaining Lord Whorfin's motives and giving an ultimatum: stop Whorfin and his army or else the Black Lectroids will protect themselves by staging a fake nuclear attack, causing the start of World War III.
With help from the Black Lectroid messenger John Parker, Banzai and the Hong Kong Cavaliers, a collection of civilian volunteers named "The Blue Blaze Irregulars" and a young woman named Penny Priddy (Ellen Barkin), a long-lost twin sister of Buckaroo's late wife, Buckaroo succeeds in his mission, destroying the Red Lectroids and saving Earth. The end credits announce an unproduced sequel Buckaroo Banzai Against the World Crime League.

Question: WHAT DID THE OSCILLATION OVERTRUSTER ALLOW THE JET CAR TO DO?
Answer: DRIVE THROUGH SOLID MATTER
Alternative answer: It allowed the jet car to drive through solid matter.