Moose And Salmon (february 1979 - Music Gallery, 1979) was a trio with Kaiser on electric guitar and trumpet player Toshinori Kondo. In Moose Kondo's minimalist, viscid and clownesque trumpet forces Kaiser to restrain his acid/psychotic soliloquies and lets Oswald's youthful madness overflow. Salmon is even noisier and even less structured, with the horns squeaking against subliminal guitar drones.

A natural outgrowth of those embryionic experiences, Alto Sax (Metalanguage, 1981) was his artistic manifesto.

A fan of pure sinusoidal tones, several of his compositions revolve around variations of that tone: Two Crossfading Stills and a Shifting Multiple Transparency (1986), Plause (1986), Tune (1989), the string quartet Spectre (1990), the Orchestral Tuning Arrangement (1994), co-composed with Linda Catlin Smith, etc.

In the meantime, though, Oswald had begun issuing the Mystery Tapes, aural collages of music, voices, and found sounds credited to Mystery Tape Laboratory. In the 1980s, the "mystery tape" aesthetics evolved into the "plunderphonics" aesthetics. A "plunderphone" is basically a "quote" of a famous piece of music, typically from popular music. In a sense, it is the musical equivalent of Andy Warhol's pop icons. A plunderphonic composition is a sonic montage of many plunderphones. The idea was first employed on the EP Plunderphonics (1988) and then on the self-produced and self-released mini-album Plunderphonics (1989), that contains 25 brief examples of what would be called "remixes" by future generations. The victims include the Beatles, Elvis Presley, Captain Beefheart, Beethoven, Liszt, James Brown, Metallica, Verdi, Stravinsky, Public Enemy, Cecil Taylor, etc. Unfortunately, legal action from a pop singer (Michael Jackson) caused most copies to be destroyed.

The EP Elektrax (Elektra, 1991) did something similar with the entire catalog of Elektra records. But the EP only contains five of the pieces that Oswald had prepared.

Discosphere (ReR, 1991) collects ballet soundtracks that employ musique concrete and plunderphonic techniques. Shane (1987) uses snippets of far-western movies. Prey (1986) is an intense collage of voices, percussion and assorted chaos. The sound of fire is protagonist of the powerful Skindling Shades (1989). Strangely, Field (1988), a frantic collage of popular American scores, achieves the poignancy of Charles Ives' sypmhonic movements. Fence (1991) toys with the voices and noises of the children of a playground, but it is unusually "musical" in the way it mixes pleasant drones and tinkling beats.

After Acoustics (august 1993 - Victo, 1993), with Henry Kaiser, Jim O'Rourke and Mari Kimura, Oswald finally returned to plunderphonics (which, in the meantime, had become an art of its own) with the ambitious plunderphonic symphony Plexure (Avant, 1993). The 24-minute piece collates more than 1,000 musical quotes. Unlike Plunderphonics, that sounded like a collection of practical jokes by a merry studio prankster, Plexure is a full-fledged "classical" composition, except that it uses quotes rather than notes as its building blocks.

The double-CD GrayFolded (Swell, 1994) applied the same idea to just one song, the Grateful Dead's Dark Star, glueing together hundreds of snippets from live performances.

The box-set Plunderphonics 69/96 (Seeland, 2001) is a career retrospective. It includes a slightly revised version of Plunderphonics, plus the entire Elektrax sessions, and most of Discosphere.

Complicité (may 2000 - Victo, 2001) is a collaboration with Paul Plimley, Marilyn Crispell and Cecil Taylor. Bloor (september 2000 - CIMP, 2001) is with David Prentice and Dominic Duval. Dearness (august 1988 - Spool, 2002) is with Anne Bourne and Fred Frith.

Later albums include: Bloor (2001), a collaboration with David Prentice and Dominic Duval; Dearness (2002), a collaboration with Anne Bourne and Fred Frith; Aparanthesi (Empreintes Digitales, 2003) for piano tuner and cello and field recordings; the 66-minute Whisperfield (2004) of whispered vocals in multiple languages; Number Nine (Emanem 4129, 2005), a collaboration with Michael Keith and Roger Turner.