"Party on"

“Party on, dudes!” was a tagline to the film Bill & Ted’s Excellent Adventure (1989) written by Chris Matheson and Ed Solomon. “Party on!” also achieved popularity in the film Wayne’s World (1992). “Party on” means that a party is going on (or should be) and that people should continue to enjoy themselves. In a work situation, “party on” means to continue doing good work.

Other “party” phrases include “party down” and “party hearty.”

Wikiquote: Bill & Ted’s Excellent Adventure
Bill & Ted’s Excellent Adventure is a 1989 film about two teenagers who utilize time travel in order to complete a history paper. It stars Keanu Reeves, Alex Winter and George Carlin.
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Taglines
. History is about to be rewritten by two guys who can’t spell…
. Time flies when you’re having fun.
. Party on, dudes!

(Oxford English Dictionary)
party, v.
intr. colloq. (orig. and chiefly U.S.). to party on: = to party down at sense 3d. Freq. in imper.
1986 C. Matheson & E. Solomon Bill & Ted’s Excellent Adventure (film script) 3 Party on, dude.
1991 M. Myers et al. Wayne’s World (film script) 6 Well, that’s all the time we have for this week. Until then, good night and party on.
2002 N.Y. Times (National ed.) 13 June a34/2 One set [of politicians] agrees that the nation is at a crossroads… The other says: Party on.

Google News Archive
5 August 1986, Milwaukee (WI) Sentinel, pt. 1, pg. 10, col. 1:
Nicaraguans suffer
while “chic” party on

OCLC WorldCat record
Party on
Author: Radiators (Musical group); Sony Music Entertainment, Inc.
Publisher: New York : Sony Music Special Products, 1995.
Edition/Format: Music CD : CD audio : English

OCLC WorldCat record
Party on! : incoming students’ expectations of their college social life
Author: Ann Groves Lloyd
Dissertation: Thesis (Ph. D.)—University of Wisconsin—Madison, 2000.
Edition/Format: Thesis/dissertation : Thesis/dissertation : Manuscript Archival Material : English

OCLC WorldCat record
Bill & Ted’s most excellent adventures. Vol. 1
Author: Evan Dorkin; Stephen DeStefano
Publisher: Amaze Ink, San Jose, CA : ©2004.
Edition/Format: Book : Fiction : English
Summary:
Collects the comic book adventures of Bill and Ted, time travelers, as they deal with robot killers, Medieval rivals, alien kidnappers, and evil record company executives.
Contents:
Bill and Ted #1: “Party on Dudes!” / inks by Stephen DeStefano ; lettering by Kurt Hathaway