Here is Hans Koessler’s beautiful Allerseelen Elegie for oboe and organ https://youtu.be/tu8HG6eYgUg
Works playable by this wonderful combination of instruments, range from the early treble and basso continuo works, Romantic oboe and piano/harmonium repertoire, and many modern works and arrangements.
Johann Ludwig Krebs’ Fantasias for oboe and organ are perhaps the most well-known pieces for this combination, such as this Fantasia in G minor: https://youtu.be/jbTt1keEdlk
The organ (particularly the chamber organ) has also been used to play basso continuo parts of unspecified instrumentation in oboe and basso continuo works by composers such as Georg Phillip Telemann and Gottfried August Homilius.
Some parts written for another (or any) treble instrument have also sometimes been played on the oboe. For example, the Sonata for Flute and Continuo composed by Anna Amalia, Princess-Abbess of Quedlinburg, has been performed on oboe and organ. https://youtu.be/-pZPMY54XJ8
The Romantic-period composition Fantaisie et variations sur "Il corsaro", Op. 54 composed by Stanislas Verroust for oboe and piano is an example of a piece which has had its piano part performed on the organ: https://youtu.be/_Sj8-IV1T_M
Similarly, Cesar Franck’s Piece No 5 from Five pieces for Harmonium which the composer had arranged for oboe and piano has been played on oboe and organ.
Another Romantic work is Otto Ernst Goepfart’s Andante religioso (alternative instruments of violin and piano or harmonium are specified). Many of Goepfart’s German compatriots have also composed for oboe and organ: Gerhard Deutschmann (Sonata di chiesa), Felix Bräuer (Aria), Bernhard Krol (Litania pastorale Op 62), Bertold Hummel (Fünf biblische Szenen Op 45), Hermann Schroeder (Sonata), and Joseph Rheinberger (Lichtenstein/Germany) (Andante pastorale).
Other composers and works include: Augustinus Franz Kropfreiter (Austria) - Drei Stücke für Oboe und Orgel, Rupert Gottfried Frieberger (Austria) – Adventsmusik, Marguerite Roesgen-Champion (Switzerland) - Nocturnes, Lionel Rogg (Switzerland) – Sonata, Gaston Litaize (France) – Diptyque, Naji Hakim (Lebanon-France) - Variations on Wie schön leuchtet der Morgenstern, David Ashley White (USA) – Canzona.
There are also a number of works written for cor anglais and organ.