I've been searching for the complete list of this great movie, including artist and song name, but haven't found any yet. All the lists I've seen show just the song names.

Could someone help me? I especially love the dark/industrial songs in the club, and the one that appears in action scenes.

This should help you out...& you're forgiven for posting a 90s question in the 80s board!  ;)

Soundtrack for Bad Influence (1990)
Please note that songs listed here (and in the movie credits) cannot always be found on CD soundtracks. Please check CD track details for confirmation.
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"SPIRITUAL HEALING"
Written by F. Hibbert
Performed by Toots
Produced by Chris Blackwell and Sly Dunbar
Courtesy of Mango Records, An Island Records Company

"CORRUPTION"
Written, Performed and Produced by Thomas Mapfumo
Courtesy of Mango Records, An Island Records Company

"HE GOT WHAT HE WANTED"
Written and Performed by Gavin Friday and The Man Seezer
Produced by Hal Willner
Courtesy of Island Records

"THE HIGHWAY"
Written by Inger Lorre and Jet Freedom
Performed by The Nymphs
Produced by Earl Mankey
Courtesy of David Geffen Company

"OUT OF THE RAIN"
Written by Tony Joe White
Performed by Etta James
Produced by Barry Beckett
Additional production: Kim Buie and Etta James
Courtesy of Island Records

"BIRD BOY"
Written by Don Charry and Nana Vasconcelos
Performed by Nana Vasconcelos and The Bushdancers
Produced by Gragg Lunsford and The Bushdancers
Courtesy of Antilles/New Directions, An Island Records Company

"ALMOST LIKE HEAVEN"
Written and Performed by Scott Cossu
Produced by George Winston
Courtesy of Windham Hill Records

"ORANE"
Written and Performed by Les Negresses Vertes
Produced by Clive Martin and Sodi
Courtesy of Sire Records/Off the Track Records
By Arrangement with Warner Special Products

"N'SEL FIK"
Written by C. Sahraoui, Fadela and R. Baba-Ahmed
Performed by Chaba Fadela
Produced by Rachid Baba-Ahmed/A Rashid and Fethi Production
Courtesy of Mango Records, An Island Records Company

"DOWNTOWN"
Written by Lloyd Cole and Blair Cowan
Performed by Lloyd Cole
Produced by Lloyd Cole, Fred Maher and Paul Hardiman
Courtesy of Polydor Ltd./Capitol Records

"WHO'S LAUGHING NOW"
Written and Performed by Skinny Puppy
Produced by David Ogilvie and cEvin Key
Courtesy of Nettwork Productions Ltd./Capitol Records

Wow! Thank you!!!  8)

However, I would define this movie as a movie of the 80's, because of the 80-ish soundtrack, 80-ish looks, and it was released on 1990 but probably shot in 1989, wasn't it?

Well, superb thriller anyway.

So that's the name of that movie. I saw it on UPN a couple of months ago and recognised both the actors but I didn't know the movie.