I do not understand this question. During and on are prepositions, not conjunctions, so they are always followed by a substantive (noun, pronoun, gerund, etc.). Most prepositions can be followed by the -ing form that is acting as a noun (gerund). During, however, cannot usually be followed by the -ing form, and students should be taught not to do so.
While and when are conjunctions.
(1) During dinner, the phone rang. NOT During we were eating dinner ...
(2) While we were eating dinner, the phone rang. NOT While dinner ...
On is a preposition that can be followed by the -ing form, but the meaning is different from that of during or while. It refers to a point in time rather than a period of time.
(3) On finishing dinner, I heard the phone ring.
(4) On the stroke of twelve, Cinderella’s gown turned back into rags.
When is a conjunction the way you are using it. It is not followed by a noun alone, but it can be followed by a noun and verb.
(5) When I finished dinner, the phone rang.
(6) When finishing dinner, I heard the phone ring.
When and while (and the preposition on) can be followed by the -ing form without an expressed subject, but the implied subject must be the same as the subject of the following clause. Otherwise you have a dangling modifier.
(6) When finishing dinner, I heard the phone ring.
(6a) NOT When finishing dinner, the phone rang.
(7) While eating dinner, we heard the phone ring.
(7a) NOT While eating dinner, the phone rang.
(8) On finishing dinner, we heard the phone ring.
(8a) NOT On finishing dinner, the phone rang.
ed. 13/05/12